2x^2-5x=288

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Solution for 2x^2-5x=288 equation:


Simplifying
2x2 + -5x = 288

Reorder the terms:
-5x + 2x2 = 288

Solving
-5x + 2x2 = 288

Solving for variable 'x'.

Reorder the terms:
-288 + -5x + 2x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + -5x + 2x2 = 0

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

Divide each side by '2'.
-144 + -2.5x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -2.5x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + -2.5x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -2.5x + x2 = 0 + 144
-2.5x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
-2.5x + x2 = 144

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 144 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 144 + 1.5625

Combine like terms: 144 + 1.5625 = 145.5625
1.5625 + -2.5x + x2 = 145.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 145.5625

Calculate the square root of the right side: 12.064928512

Break this problem into two subproblems by setting 
(x + -1.25) equal to 12.064928512 and -12.064928512.

Subproblem 1

x + -1.25 = 12.064928512 Simplifying x + -1.25 = 12.064928512 Reorder the terms: -1.25 + x = 12.064928512 Solving -1.25 + x = 12.064928512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 12.064928512 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 12.064928512 + 1.25 x = 12.064928512 + 1.25 Combine like terms: 12.064928512 + 1.25 = 13.314928512 x = 13.314928512 Simplifying x = 13.314928512

Subproblem 2

x + -1.25 = -12.064928512 Simplifying x + -1.25 = -12.064928512 Reorder the terms: -1.25 + x = -12.064928512 Solving -1.25 + x = -12.064928512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -12.064928512 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -12.064928512 + 1.25 x = -12.064928512 + 1.25 Combine like terms: -12.064928512 + 1.25 = -10.814928512 x = -10.814928512 Simplifying x = -10.814928512

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.314928512, -10.814928512}

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