2x^2=x+9

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


Simplifying
2x2 = x + 9

Reorder the terms:
2x2 = 9 + x

Solving
2x2 = 9 + x

Solving for variable 'x'.

Reorder the terms:
-9 + -1x + 2x2 = 9 + x + -9 + -1x

Reorder the terms:
-9 + -1x + 2x2 = 9 + -9 + x + -1x

Combine like terms: 9 + -9 = 0
-9 + -1x + 2x2 = 0 + x + -1x
-9 + -1x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-9 + -1x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -0.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -0.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -0.5x + x2 = 0 + 4.5
-0.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-0.5x + x2 = 4.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 4.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 4.5 + 0.0625

Combine like terms: 4.5 + 0.0625 = 4.5625
0.0625 + -0.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + -0.25 = 2.136000936 Simplifying x + -0.25 = 2.136000936 Reorder the terms: -0.25 + x = 2.136000936 Solving -0.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.136000936 + 0.25 x = 2.136000936 + 0.25 Combine like terms: 2.136000936 + 0.25 = 2.386000936 x = 2.386000936 Simplifying x = 2.386000936

Subproblem 2

x + -0.25 = -2.136000936 Simplifying x + -0.25 = -2.136000936 Reorder the terms: -0.25 + x = -2.136000936 Solving -0.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.136000936 + 0.25 x = -2.136000936 + 0.25 Combine like terms: -2.136000936 + 0.25 = -1.886000936 x = -1.886000936 Simplifying x = -1.886000936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.386000936, -1.886000936}

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