(4x+3)(x-8)=90

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Solution for (4x+3)(x-8)=90 equation:


Simplifying
(4x + 3)(x + -8) = 90

Reorder the terms:
(3 + 4x)(x + -8) = 90

Reorder the terms:
(3 + 4x)(-8 + x) = 90

Multiply (3 + 4x) * (-8 + x)
(3(-8 + x) + 4x * (-8 + x)) = 90
((-8 * 3 + x * 3) + 4x * (-8 + x)) = 90
((-24 + 3x) + 4x * (-8 + x)) = 90
(-24 + 3x + (-8 * 4x + x * 4x)) = 90
(-24 + 3x + (-32x + 4x2)) = 90

Combine like terms: 3x + -32x = -29x
(-24 + -29x + 4x2) = 90

Solving
-24 + -29x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
-24 + -90 + -29x + 4x2 = 90 + -90

Combine like terms: -24 + -90 = -114
-114 + -29x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-114 + -29x + 4x2 = 0

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

Divide each side by '4'.
-28.5 + -7.25x + x2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + -7.25x + 28.5 + x2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + -7.25x + x2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + -7.25x + x2 = 0 + 28.5
-7.25x + x2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
-7.25x + x2 = 28.5

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = 28.5 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = 28.5 + 13.140625

Combine like terms: 28.5 + 13.140625 = 41.640625
13.140625 + -7.25x + x2 = 41.640625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 41.640625

Calculate the square root of the right side: 6.45295475

Break this problem into two subproblems by setting 
(x + -3.625) equal to 6.45295475 and -6.45295475.

Subproblem 1

x + -3.625 = 6.45295475 Simplifying x + -3.625 = 6.45295475 Reorder the terms: -3.625 + x = 6.45295475 Solving -3.625 + x = 6.45295475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 6.45295475 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 6.45295475 + 3.625 x = 6.45295475 + 3.625 Combine like terms: 6.45295475 + 3.625 = 10.07795475 x = 10.07795475 Simplifying x = 10.07795475

Subproblem 2

x + -3.625 = -6.45295475 Simplifying x + -3.625 = -6.45295475 Reorder the terms: -3.625 + x = -6.45295475 Solving -3.625 + x = -6.45295475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -6.45295475 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -6.45295475 + 3.625 x = -6.45295475 + 3.625 Combine like terms: -6.45295475 + 3.625 = -2.82795475 x = -2.82795475 Simplifying x = -2.82795475

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.07795475, -2.82795475}

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