(2x-3)(x)=317

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Solution for (2x-3)(x)=317 equation:


Simplifying
(2x + -3)(x) = 317

Reorder the terms:
(-3 + 2x)(x) = 317

Reorder the terms for easier multiplication:
x(-3 + 2x) = 317
(-3 * x + 2x * x) = 317
(-3x + 2x2) = 317

Solving
-3x + 2x2 = 317

Solving for variable 'x'.

Reorder the terms:
-317 + -3x + 2x2 = 317 + -317

Combine like terms: 317 + -317 = 0
-317 + -3x + 2x2 = 0

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

Divide each side by '2'.
-158.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '158.5' to each side of the equation.
-158.5 + -1.5x + 158.5 + x2 = 0 + 158.5

Reorder the terms:
-158.5 + 158.5 + -1.5x + x2 = 0 + 158.5

Combine like terms: -158.5 + 158.5 = 0.0
0.0 + -1.5x + x2 = 0 + 158.5
-1.5x + x2 = 0 + 158.5

Combine like terms: 0 + 158.5 = 158.5
-1.5x + x2 = 158.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 158.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 158.5 + 0.5625

Combine like terms: 158.5 + 0.5625 = 159.0625
0.5625 + -1.5x + x2 = 159.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 159.0625

Calculate the square root of the right side: 12.611998256

Break this problem into two subproblems by setting 
(x + -0.75) equal to 12.611998256 and -12.611998256.

Subproblem 1

x + -0.75 = 12.611998256 Simplifying x + -0.75 = 12.611998256 Reorder the terms: -0.75 + x = 12.611998256 Solving -0.75 + x = 12.611998256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 12.611998256 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 12.611998256 + 0.75 x = 12.611998256 + 0.75 Combine like terms: 12.611998256 + 0.75 = 13.361998256 x = 13.361998256 Simplifying x = 13.361998256

Subproblem 2

x + -0.75 = -12.611998256 Simplifying x + -0.75 = -12.611998256 Reorder the terms: -0.75 + x = -12.611998256 Solving -0.75 + x = -12.611998256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -12.611998256 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -12.611998256 + 0.75 x = -12.611998256 + 0.75 Combine like terms: -12.611998256 + 0.75 = -11.861998256 x = -11.861998256 Simplifying x = -11.861998256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.361998256, -11.861998256}

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