(2x-7)(x+8)=1152

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Solution for (2x-7)(x+8)=1152 equation: 


Simplifying
(2x + -7)(x + 8) = 1152

Reorder the terms:
(-7 + 2x)(x + 8) = 1152

Reorder the terms:
(-7 + 2x)(8 + x) = 1152

Multiply (-7 + 2x) * (8 + x)
(-7(8 + x) + 2x * (8 + x)) = 1152
((8 * -7 + x * -7) + 2x * (8 + x)) = 1152
((-56 + -7x) + 2x * (8 + x)) = 1152
(-56 + -7x + (8 * 2x + x * 2x)) = 1152
(-56 + -7x + (16x + 2x2)) = 1152

Combine like terms: -7x + 16x = 9x
(-56 + 9x + 2x2) = 1152

Solving
-56 + 9x + 2x2 = 1152

Solving for variable 'x'.

Reorder the terms:
-56 + -1152 + 9x + 2x2 = 1152 + -1152

Combine like terms: -56 + -1152 = -1208
-1208 + 9x + 2x2 = 1152 + -1152

Combine like terms: 1152 + -1152 = 0
-1208 + 9x + 2x2 = 0

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

Divide each side by '2'.
-604 + 4.5x + x2 = 0

Move the constant term to the right:

Add '604' to each side of the equation.
-604 + 4.5x + 604 + x2 = 0 + 604

Reorder the terms:
-604 + 604 + 4.5x + x2 = 0 + 604

Combine like terms: -604 + 604 = 0
0 + 4.5x + x2 = 0 + 604
4.5x + x2 = 0 + 604

Combine like terms: 0 + 604 = 604
4.5x + x2 = 604

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 604 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 604 + 5.0625

Combine like terms: 604 + 5.0625 = 609.0625
5.0625 + 4.5x + x2 = 609.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 609.0625

Calculate the square root of the right side: 24.67919164

Break this problem into two subproblems by setting 
(x + 2.25) equal to 24.67919164 and -24.67919164.


Subproblem 1
x + 2.25 = 24.67919164

Simplifying
x + 2.25 = 24.67919164

Reorder the terms:
2.25 + x = 24.67919164

Solving
2.25 + x = 24.67919164

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 24.67919164 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 24.67919164 + -2.25
x = 24.67919164 + -2.25

Combine like terms: 24.67919164 + -2.25 = 22.42919164
x = 22.42919164

Simplifying
x = 22.42919164


Subproblem 2
x + 2.25 = -24.67919164

Simplifying
x + 2.25 = -24.67919164

Reorder the terms:
2.25 + x = -24.67919164

Solving
2.25 + x = -24.67919164

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -24.67919164 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -24.67919164 + -2.25
x = -24.67919164 + -2.25

Combine like terms: -24.67919164 + -2.25 = -26.92919164
x = -26.92919164

Simplifying
x = -26.92919164


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.42919164, -26.92919164}

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