how to solve 3x^2 + 10x = -6?

Question

please help i dont understand!

Answer 1

3x^2 + 10x = -6
3x^2+10x+6=0
Compare above equation with a.x^2+b.x+c=0
which are having roots,
x=(-b±√(b^2-4*a*c))/2*a
Here,
a=3,b=10 and c=6.So,

x=(-10±√(100-4*3*6))/6
x=(-10±√(100-72))/6
x=(-10±√28)/6
x=(-10+2√7)/6
x=-0.785
x=(-10-2√7)/6
x=-2.549

Answer 2

Move everything to the left side, so that the right side equals 0. Do this by adding 6 to both sides:

3x²+10x+6=0

You can determine the solutions with the Quadratic Formula. For the equation ax²+bx+c=0, x=(-b­±√(b²-4ac))/2a. In this case, a=3, b=10, and c=6:

x=(-10±√(10²-4*3*6))/2*3
=(-10±√(100-72))/6
=(-10±√28)/6
=(-10±2√7)/6
x=(-5+√7)/3 or x=(-5-√7)/3

Answer 3

Add 6 to both sides: you get 3x^2+10x+6=0.

When you have an equation ax^2+bx+c=0 its solutions are (-b+(b^2-4ac)^(1/2))/(2a) and (-b-(b^2-4ac)^(1/2))/2a.

In your case a=3, b=10, c=6. Apply the formula to your equation and find:

(-10+(100-4*3*6)^(1/2))/(2*3) = (-10+(100-72)^(1/2))/6 = (-10+36^(1/2))/6 = (-10+2*7^(1/2))/6
and

(-10-(100-4*3*6)^(1/2))/(2*3) = (-10-2*7^(1/2))/6

Answer 4

Simplifying
3x2 + 10x = -6

Reorder the terms:
10x + 3x2 = -6

Solving
10x + 3x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 10x + 3x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 10x + 3x2 = 0

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

Divide each side by '3'.
2 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 3.333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.333333333x + x2 = 0 + -2
3.333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.333333333x + x2 = -2

The x term is 3.333333333x. Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -2 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -2 + 2.777777779

Combine like terms: -2 + 2.777777779 = 0.777777779
2.777777779 + 3.333333333x + x2 = 0.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 0.777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting
(x + 1.666666667) equal to 0.881917104 and -0.881917104.

Subproblem 1x + 1.666666667 = 0.881917104

Simplifying
x + 1.666666667 = 0.881917104

Reorder the terms:
1.666666667 + x = 0.881917104

Solving
1.666666667 + x = 0.881917104

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 0.881917104 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 0.881917104 + -1.666666667
x = 0.881917104 + -1.666666667

Combine like terms: 0.881917104 + -1.666666667 = -0.784749563
x = -0.784749563

Simplifying
x = -0.784749563

Subproblem 2x + 1.666666667 = -0.881917104

Simplifying
x + 1.666666667 = -0.881917104

Reorder the terms:
1.666666667 + x = -0.881917104

Solving
1.666666667 + x = -0.881917104

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -0.881917104 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -0.881917104 + -1.666666667
x = -0.881917104 + -1.666666667

Combine like terms: -0.881917104 + -1.666666667 = -2.548583771
x = -2.548583771

Simplifying
x = -2.548583771

Solution

The solution to the problem is based on the solutions
from the subproblems.

x = {-0.784749563, -2.548583771}
or
x = {-39/50, -2 5/9}

Answer 5

3x^2 + 10x = -6 add 6 to each side
3x^2+10x+6=0
x=(-10±√(100-4*3*6))/6
x=(-10±√(100-72))/6
x=(-10±√28)/6
x=(-10+2√7)/6=-0.78474956297846980316612808212025
x=(-10-2√7)/6=-2.5485837703548635301672052512131

Answer 6

put in standard form

3x^2+10x+6 = 0

Quadratic Formula with a=3, b=10, c=6

-10 (+ or -) Sqrt(28) divided by 6

reduces to -5 (+ or -) sqrt(7) divided by 3

(+ or -) means plus or minus sign

Answer 7

3x^2+10x= - 6

re arranging them we get

3x^2-10x+6=0

now compare this quadratic eqn. with a standard eqn.

ax^2+bx+c=o

now u have two values of x one is

x1= (-b+d^1/2)/ 2a ......................... Eqn. NO. A

other value is

x2=(-b-d^1/2)/2a ........................ Eqn No B


where
d= b^2-4.a.c

here . means multiplication

so in ur case

a=3, b=10 and c=6

so we get
d= (10)^2 - 4 . 3 . 6

d= 100-72
d=28

now subsituting the value of d in eqn. no. A

x1=(-b+d^1/2)/2a

x1=(-10+ 28^1/2)/ 2 . 3

now solving for x

x1= (-10+5.3)/6
x1= - 4.7/6
x1= - 0.78

now subsitute the value of d in eqn no. B

x2=(-b-d^1/2)/2 . a
x2=(-10-5.3)/6
x2= - 15.3/6
x2= - 2.55

so the values of x are - 0.78 and - 2.55
so whenever u get a question on quadratic eqn.
solve it like this if u r not able to get the roots or it doesnot have a real roots.

remember the 2 formulas

Ax^2+Bx+C=0
or
Ax^2+Bx-C=0

D= B^2 - 4 .A .C

X1= (-B+D^1/2)/ 2. A

X2= (-B-D^1/2)/2 .A


HOPE U UNDERSTAND IT

Answer 8

3x^2 + 10x + 6 = 0

use quadratic formula

x = [-b+-sqrt(b^2 - 4ac)]/2a

in your case a =3, b = 10, c = 6

x = [-10+-sqrt(100-4*6*3)]/6

x = [-10 +- sqrt28]/6

Answer 9

3x^2+10x+6=0 (add 6 to both sides)
use quadratic formula:
x=[-b+/-sqrt(b^2-4ac)]/2a
x=[-10+/-√(100-72)]/6
x=[-10+/-2√7]/6
x=(-5-√7)/3
or x= (-5+√7)/3

Answer 10

3x^2+10x+6=0
-.78475
-2.5486
or
-10+or-sqrt(28)/6