-13=9x-2x^2

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Solution for -13=9x-2x^2 equation:


Simplifying
-13 = 9x + -2x2

Solving
-13 = 9x + -2x2

Solving for variable 'x'.

Reorder the terms:
-13 + -9x + 2x2 = 9x + -9x + -2x2 + 2x2

Combine like terms: 9x + -9x = 0
-13 + -9x + 2x2 = 0 + -2x2 + 2x2
-13 + -9x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-13 + -9x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -4.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -4.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -4.5x + x2 = 0 + 6.5
-4.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-4.5x + x2 = 6.5

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 = 6.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 6.5 + 5.0625

Combine like terms: 6.5 + 5.0625 = 11.5625
5.0625 + -4.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.400367627 and -3.400367627.

Subproblem 1

x + -2.25 = 3.400367627 Simplifying x + -2.25 = 3.400367627 Reorder the terms: -2.25 + x = 3.400367627 Solving -2.25 + x = 3.400367627 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 = 3.400367627 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.400367627 + 2.25 x = 3.400367627 + 2.25 Combine like terms: 3.400367627 + 2.25 = 5.650367627 x = 5.650367627 Simplifying x = 5.650367627

Subproblem 2

x + -2.25 = -3.400367627 Simplifying x + -2.25 = -3.400367627 Reorder the terms: -2.25 + x = -3.400367627 Solving -2.25 + x = -3.400367627 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 = -3.400367627 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.400367627 + 2.25 x = -3.400367627 + 2.25 Combine like terms: -3.400367627 + 2.25 = -1.150367627 x = -1.150367627 Simplifying x = -1.150367627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.650367627, -1.150367627}

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