(4x+7)(x-8)=8

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Solution for (4x+7)(x-8)=8 equation:


Simplifying
(4x + 7)(x + -8) = 8

Reorder the terms:
(7 + 4x)(x + -8) = 8

Reorder the terms:
(7 + 4x)(-8 + x) = 8

Multiply (7 + 4x) * (-8 + x)
(7(-8 + x) + 4x * (-8 + x)) = 8
((-8 * 7 + x * 7) + 4x * (-8 + x)) = 8
((-56 + 7x) + 4x * (-8 + x)) = 8
(-56 + 7x + (-8 * 4x + x * 4x)) = 8
(-56 + 7x + (-32x + 4x2)) = 8

Combine like terms: 7x + -32x = -25x
(-56 + -25x + 4x2) = 8

Solving
-56 + -25x + 4x2 = 8

Solving for variable 'x'.

Reorder the terms:
-56 + -8 + -25x + 4x2 = 8 + -8

Combine like terms: -56 + -8 = -64
-64 + -25x + 4x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-64 + -25x + 4x2 = 0

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

Divide each side by '4'.
-16 + -6.25x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -6.25x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -6.25x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -6.25x + x2 = 0 + 16
-6.25x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-6.25x + x2 = 16

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 16 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 16 + 9.765625

Combine like terms: 16 + 9.765625 = 25.765625
9.765625 + -6.25x + x2 = 25.765625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 25.765625

Calculate the square root of the right side: 5.075985126

Break this problem into two subproblems by setting 
(x + -3.125) equal to 5.075985126 and -5.075985126.

Subproblem 1

x + -3.125 = 5.075985126 Simplifying x + -3.125 = 5.075985126 Reorder the terms: -3.125 + x = 5.075985126 Solving -3.125 + x = 5.075985126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 5.075985126 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 5.075985126 + 3.125 x = 5.075985126 + 3.125 Combine like terms: 5.075985126 + 3.125 = 8.200985126 x = 8.200985126 Simplifying x = 8.200985126

Subproblem 2

x + -3.125 = -5.075985126 Simplifying x + -3.125 = -5.075985126 Reorder the terms: -3.125 + x = -5.075985126 Solving -3.125 + x = -5.075985126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -5.075985126 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -5.075985126 + 3.125 x = -5.075985126 + 3.125 Combine like terms: -5.075985126 + 3.125 = -1.950985126 x = -1.950985126 Simplifying x = -1.950985126

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.200985126, -1.950985126}

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