Quadratic Formula?

Question

Solve by using the quadratic formula.

x^2=7x+6

Answer 1

x² - 7x - 6 = 0
x = [ 7 ± √(49 + 24)] / 2
x = [ 7 ± √(73) ] / 2

Answer 2

The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac))/2a.
So we just plug the figures in the standard quadratic equation (ax^2 + bx + c) into the quadratic formula and solve.
x^2 = 7x + 6
x^2 - 7x - 6 = 0
x = (7 +/- sqrt(-7^2 - 4(1(-6)))/2(1)
x = (7 +/- sqrt(49 + 24))/2
x = (7 +/- sqrt(73))/2
x = (7 +/- sqrt73)/2

Answer 3

Simplifying
x^2 = 7x + 6

Reorder the terms:
x^2 = 6 + 7x

Solving
x^2 = 6 + 7x

Solving for variable 'x'.

Reorder the terms:
-6 + -7x + x^2 = 6 + 7x + -6 + -7x

Reorder the terms:
-6 + -7x + x^2 = 6 + -6 + 7x + -7x

Combine like terms: 6 + -6 = 0
-6 + -7x + x^2 = 0 + 7x + -7x
-6 + -7x + x^2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6 + -7x + x^2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7x + 6 + x^2 = 0 + 6

Reorder the terms:
-6 + 6 + -7x + x^2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7x + x^2 = 0 + 6
-7x + x^2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7x + x^2 = 6

The x term is -7x. Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + -7x + x^2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7x + x^2 = 18.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting
(x + -3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + -3.5 = 4.272001873

Simplifying
x + -3.5 = 4.272001873

Reorder the terms:
-3.5 + x = 4.272001873

Solving
-3.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.272001873 + 3.5
x = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
x = 7.772001873

Simplifying
x = 7.772001873

Subproblem 2
x + -3.5 = -4.272001873

Simplifying
x + -3.5 = -4.272001873

Reorder the terms:
-3.5 + x = -4.272001873

Solving
-3.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.272001873 + 3.5
x = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
x = -0.772001873

Simplifying
x = -0.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.772001873, -0.772001873}

Answer 4

x^2=7x+6
x^2-7x-6

plug into -b +- SR b^2 -4ac all divided by 2a
-(-7) +- SR (-7)^2 -4(1)(-6) //2(1)
7+- SR 49+24 //2
7 +- SR 73 //2
(7+8.54)/2......(7-8.54)/2
x=7.77 x= -.77

Answer 5

x^2=7x+6
x² - 7x - 6 = 0

........ -b ± √(b² - 4ac)
x = ---------------------
. . . . . . 2a

In the given problem, a = 1, b = (-7), c = (-6)

. . . . -(-7) ± √{(-7)² - 4*1*(-6)
x = ..---------------------------------
. . . . . . . . . . (2*1)

. . . . . .7 ± √{49 +24}
x = . .------------------------
. . . . . . . . . . .2

. . . . . . . 7 ± √ 73
x = . . . -------------
. . . . . . . . . 2

. . . . . . . .7+ 8.54
x = . . . . .----------- = (15.54/2) = 7.77
. . . . . . . . . . .2. . .. . . . .. . . . .. . ======

. . . . . . . . . . . . . OR

. . . . . . . . 7 - 8.54
x = . . . . . .----------- . =(-1.54/2) = - .77
. . . . . . . . . . . 2 . . . . . . . . . . . . . .=====

Answer 6

Get everything on the left:
x² - 7x - 6 = 0

a = 1, b = -7, c = -6

...... -b +/- sqrt( b² - 4ac )
x = -----------------------------
............... 2a

...... 7 +/- sqrt( (-7)² - 4(1)(-6) )
x = ------------------------------------
............... 2(1)

...... 7 +/- sqrt( 49 + 24 )
x = ----------------------------
............... 2

...... 7 +/- sqrt( 73 )
x = ---------------------
............... 2