(4x+9)(x-4)-8x+18=0

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Solution for (4x+9)(x-4)-8x+18=0 equation:


Simplifying
(4x + 9)(x + -4) + -8x + 18 = 0

Reorder the terms:
(9 + 4x)(x + -4) + -8x + 18 = 0

Reorder the terms:
(9 + 4x)(-4 + x) + -8x + 18 = 0

Multiply (9 + 4x) * (-4 + x)
(9(-4 + x) + 4x * (-4 + x)) + -8x + 18 = 0
((-4 * 9 + x * 9) + 4x * (-4 + x)) + -8x + 18 = 0
((-36 + 9x) + 4x * (-4 + x)) + -8x + 18 = 0
(-36 + 9x + (-4 * 4x + x * 4x)) + -8x + 18 = 0
(-36 + 9x + (-16x + 4x2)) + -8x + 18 = 0

Combine like terms: 9x + -16x = -7x
(-36 + -7x + 4x2) + -8x + 18 = 0

Reorder the terms:
-36 + 18 + -7x + -8x + 4x2 = 0

Combine like terms: -36 + 18 = -18
-18 + -7x + -8x + 4x2 = 0

Combine like terms: -7x + -8x = -15x
-18 + -15x + 4x2 = 0

Solving
-18 + -15x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-4.5 + -3.75x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -3.75x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -3.75x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -3.75x + x2 = 0 + 4.5
-3.75x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-3.75x + x2 = 4.5

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 4.5 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 4.5 + 3.515625

Combine like terms: 4.5 + 3.515625 = 8.015625
3.515625 + -3.75x + x2 = 8.015625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 8.015625

Calculate the square root of the right side: 2.831187913

Break this problem into two subproblems by setting 
(x + -1.875) equal to 2.831187913 and -2.831187913.

Subproblem 1

x + -1.875 = 2.831187913 Simplifying x + -1.875 = 2.831187913 Reorder the terms: -1.875 + x = 2.831187913 Solving -1.875 + x = 2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.831187913 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.831187913 + 1.875 x = 2.831187913 + 1.875 Combine like terms: 2.831187913 + 1.875 = 4.706187913 x = 4.706187913 Simplifying x = 4.706187913

Subproblem 2

x + -1.875 = -2.831187913 Simplifying x + -1.875 = -2.831187913 Reorder the terms: -1.875 + x = -2.831187913 Solving -1.875 + x = -2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.831187913 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.831187913 + 1.875 x = -2.831187913 + 1.875 Combine like terms: -2.831187913 + 1.875 = -0.956187913 x = -0.956187913 Simplifying x = -0.956187913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.706187913, -0.956187913}

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