9x^2-256x=-284

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Solution for 9x^2-256x=-284 equation:


Simplifying
9x2 + -256x = -284

Reorder the terms:
-256x + 9x2 = -284

Solving
-256x + 9x2 = -284

Solving for variable 'x'.

Reorder the terms:
284 + -256x + 9x2 = -284 + 284

Combine like terms: -284 + 284 = 0
284 + -256x + 9x2 = 0

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

Divide each side by '9'.
31.55555556 + -28.44444444x + x2 = 0

Move the constant term to the right:

Add '-31.55555556' to each side of the equation.
31.55555556 + -28.44444444x + -31.55555556 + x2 = 0 + -31.55555556

Reorder the terms:
31.55555556 + -31.55555556 + -28.44444444x + x2 = 0 + -31.55555556

Combine like terms: 31.55555556 + -31.55555556 = 0.00000000
0.00000000 + -28.44444444x + x2 = 0 + -31.55555556
-28.44444444x + x2 = 0 + -31.55555556

Combine like terms: 0 + -31.55555556 = -31.55555556
-28.44444444x + x2 = -31.55555556

The x term is -28.44444444x.  Take half its coefficient (-14.22222222).
Square it (202.2716049) and add it to both sides.

Add '202.2716049' to each side of the equation.
-28.44444444x + 202.2716049 + x2 = -31.55555556 + 202.2716049

Reorder the terms:
202.2716049 + -28.44444444x + x2 = -31.55555556 + 202.2716049

Combine like terms: -31.55555556 + 202.2716049 = 170.71604934
202.2716049 + -28.44444444x + x2 = 170.71604934

Factor a perfect square on the left side:
(x + -14.22222222)(x + -14.22222222) = 170.71604934

Calculate the square root of the right side: 13.065835195

Break this problem into two subproblems by setting 
(x + -14.22222222) equal to 13.065835195 and -13.065835195.

Subproblem 1

x + -14.22222222 = 13.065835195 Simplifying x + -14.22222222 = 13.065835195 Reorder the terms: -14.22222222 + x = 13.065835195 Solving -14.22222222 + x = 13.065835195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.22222222' to each side of the equation. -14.22222222 + 14.22222222 + x = 13.065835195 + 14.22222222 Combine like terms: -14.22222222 + 14.22222222 = 0.00000000 0.00000000 + x = 13.065835195 + 14.22222222 x = 13.065835195 + 14.22222222 Combine like terms: 13.065835195 + 14.22222222 = 27.288057415 x = 27.288057415 Simplifying x = 27.288057415

Subproblem 2

x + -14.22222222 = -13.065835195 Simplifying x + -14.22222222 = -13.065835195 Reorder the terms: -14.22222222 + x = -13.065835195 Solving -14.22222222 + x = -13.065835195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.22222222' to each side of the equation. -14.22222222 + 14.22222222 + x = -13.065835195 + 14.22222222 Combine like terms: -14.22222222 + 14.22222222 = 0.00000000 0.00000000 + x = -13.065835195 + 14.22222222 x = -13.065835195 + 14.22222222 Combine like terms: -13.065835195 + 14.22222222 = 1.156387025 x = 1.156387025 Simplifying x = 1.156387025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.288057415, 1.156387025}

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