-9x+2x^2=467

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Solution for -9x+2x^2=467 equation:


Simplifying
-9x + 2x2 = 467

Solving
-9x + 2x2 = 467

Solving for variable 'x'.

Reorder the terms:
-467 + -9x + 2x2 = 467 + -467

Combine like terms: 467 + -467 = 0
-467 + -9x + 2x2 = 0

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

Divide each side by '2'.
-233.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '233.5' to each side of the equation.
-233.5 + -4.5x + 233.5 + x2 = 0 + 233.5

Reorder the terms:
-233.5 + 233.5 + -4.5x + x2 = 0 + 233.5

Combine like terms: -233.5 + 233.5 = 0.0
0.0 + -4.5x + x2 = 0 + 233.5
-4.5x + x2 = 0 + 233.5

Combine like terms: 0 + 233.5 = 233.5
-4.5x + x2 = 233.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 233.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 233.5 + 5.0625

Combine like terms: 233.5 + 5.0625 = 238.5625
5.0625 + -4.5x + x2 = 238.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 238.5625

Calculate the square root of the right side: 15.445468591

Break this problem into two subproblems by setting 
(x + -2.25) equal to 15.445468591 and -15.445468591.

Subproblem 1

x + -2.25 = 15.445468591 Simplifying x + -2.25 = 15.445468591 Reorder the terms: -2.25 + x = 15.445468591 Solving -2.25 + x = 15.445468591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 15.445468591 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 15.445468591 + 2.25 x = 15.445468591 + 2.25 Combine like terms: 15.445468591 + 2.25 = 17.695468591 x = 17.695468591 Simplifying x = 17.695468591

Subproblem 2

x + -2.25 = -15.445468591 Simplifying x + -2.25 = -15.445468591 Reorder the terms: -2.25 + x = -15.445468591 Solving -2.25 + x = -15.445468591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -15.445468591 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -15.445468591 + 2.25 x = -15.445468591 + 2.25 Combine like terms: -15.445468591 + 2.25 = -13.195468591 x = -13.195468591 Simplifying x = -13.195468591

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.695468591, -13.195468591}

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