2x^2+3x=256

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Solution for 2x^2+3x=256 equation:


Simplifying
2x2 + 3x = 256

Reorder the terms:
3x + 2x2 = 256

Solving
3x + 2x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 3x + 2x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 3x + 2x2 = 0

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

Divide each side by '2'.
-128 + 1.5x + x2 = 0

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 1.5x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + 1.5x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 1.5x + x2 = 0 + 128
1.5x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
1.5x + x2 = 128

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 = 128 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 128 + 0.5625

Combine like terms: 128 + 0.5625 = 128.5625
0.5625 + 1.5x + x2 = 128.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 128.5625

Calculate the square root of the right side: 11.33854047

Break this problem into two subproblems by setting 
(x + 0.75) equal to 11.33854047 and -11.33854047.

Subproblem 1

x + 0.75 = 11.33854047 Simplifying x + 0.75 = 11.33854047 Reorder the terms: 0.75 + x = 11.33854047 Solving 0.75 + x = 11.33854047 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 = 11.33854047 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 11.33854047 + -0.75 x = 11.33854047 + -0.75 Combine like terms: 11.33854047 + -0.75 = 10.58854047 x = 10.58854047 Simplifying x = 10.58854047

Subproblem 2

x + 0.75 = -11.33854047 Simplifying x + 0.75 = -11.33854047 Reorder the terms: 0.75 + x = -11.33854047 Solving 0.75 + x = -11.33854047 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 = -11.33854047 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -11.33854047 + -0.75 x = -11.33854047 + -0.75 Combine like terms: -11.33854047 + -0.75 = -12.08854047 x = -12.08854047 Simplifying x = -12.08854047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.58854047, -12.08854047}

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