Quadratic equations...?

Question

Having trouble with these...

y^2 + 16y + 55 = 0

x^2 + 26x + 5 = -20

6y^2 + 10y - 3 = 8y

Answer 1

y^2 + 16y + 55 = 0
(y+11)(y+5) = 55
y = -11, -5

x^2 + 26x + 5 = -20
x^2+26x +25 =0
(x+25)(x+1) = 0
x = -25, -1

6y^2 + 10y - 3 = 8y
6y^2+2y -3 = 0
y = [-2 +/- sqrt(2^2-4(6)(-3)0]/(2*6)
y = [-2 +/- sqrt(76)]/12
y = [-1 +/- sqrt(19)]/6

Answer 2

1) Simplifying
y2 + 16y + 55 = 0

Reorder the terms:
55 + 16y + y2 = 0

Solving
55 + 16y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(11 + y)(5 + y) = 0

Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11

Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {-11, -5}

2) Simplifying
x2 + 26x + 5 = -20

Reorder the terms:
5 + 26x + x2 = -20

Solving
5 + 26x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
5 + 20 + 26x + x2 = -20 + 20

Combine like terms: 5 + 20 = 25
25 + 26x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
25 + 26x + x2 = 0

Factor a trinomial.
(25 + x)(1 + x) = 0


Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25

Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-25, -1}

3) Simplifying
6y2 + 10y + -3 = 8y

Reorder the terms:
-3 + 10y + 6y2 = 8y

Solving
-3 + 10y + 6y2 = 8y

Solving for variable 'y'.

Reorder the terms:
-3 + 10y + -8y + 6y2 = 8y + -8y

Combine like terms: 10y + -8y = 2y
-3 + 2y + 6y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-3 + 2y + 6y2 = 0

Begin completing the square. Divide all terms by
6 the coefficient of the squared term:

Divide each side by '6'.
-0.5 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3333333333y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3333333333y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3333333333y + y2 = 0 + 0.5
0.3333333333y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3333333333y + y2 = 0.5

The y term is 0.3333333333y. Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333y + 0.02777777779 + y2 = 0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333y + y2 = 0.5 + 0.02777777779

Combine like terms: 0.5 + 0.02777777779 = 0.52777777779
0.02777777779 + 0.3333333333y + y2 = 0.52777777779

Factor a perfect square on the left side:
(y + 0.1666666667)(y + 0.1666666667) = 0.52777777779

Calculate the square root of the right side: 0.726483157

Break this problem into two subproblems by setting
(y + 0.1666666667) equal to 0.726483157 and -0.726483157.


y + 0.1666666667 = 0.726483157

Simplifying
y + 0.1666666667 = 0.726483157

Reorder the terms:
0.1666666667 + y = 0.726483157

Solving
0.1666666667 + y = 0.726483157

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + y = 0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + y = 0.726483157 + -0.1666666667
y = 0.726483157 + -0.1666666667

Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903
y = 0.5598164903

Simplifying
y = 0.5598164903


y + 0.1666666667 = -0.726483157

Simplifying
y + 0.1666666667 = -0.726483157

Reorder the terms:
0.1666666667 + y = -0.726483157

Solving
0.1666666667 + y = -0.726483157

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + y = -0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + y = -0.726483157 + -0.1666666667
y = -0.726483157 + -0.1666666667

Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237
y = -0.8931498237

Simplifying
y = -0.8931498237

Solution

y = {0.5598164903, -0.8931498237}

Answer 3

I assume you are trying to find the roots of these equations.

Method 1: Use the quadratic formula, it is in your book. For the first equation a = 1 b= 16 c = 55. SUbstitute numbers into formula.

Method 2: Graph the equation using Excel. For the first equation f(y) = y^2+16y=55. The roots are where this equation crosses the x axis.

Answer 4

1) (y+5)(y+11)=0
y=-5, y=-11

2)x^2+26+25=0
(x+1)(x+25)=0
x=-1 , x=-25

3) 6y^2+2y-3=0
Use quadratic
y=(-2+/-sqroot(2^2-(4*6*-3))) /(6*2) = (-2+/-sqr76)/12
So, y=(-2+sqr76)/12 and y=(-2-sqr76)/12.

sqr means squareroot.