10x-13=37+20x^2

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Solution for 10x-13=37+20x^2 equation:


Simplifying
10x + -13 = 37 + 20x2

Reorder the terms:
-13 + 10x = 37 + 20x2

Solving
-13 + 10x = 37 + 20x2

Solving for variable 'x'.

Reorder the terms:
-13 + -37 + 10x + -20x2 = 37 + 20x2 + -37 + -20x2

Combine like terms: -13 + -37 = -50
-50 + 10x + -20x2 = 37 + 20x2 + -37 + -20x2

Reorder the terms:
-50 + 10x + -20x2 = 37 + -37 + 20x2 + -20x2

Combine like terms: 37 + -37 = 0
-50 + 10x + -20x2 = 0 + 20x2 + -20x2
-50 + 10x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-50 + 10x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + x + -2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-5 + x + -2x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + -2x2 = 0

Solving
-5 + x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5x + x2 = 0 + -2.5
-0.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5x + x2 = -2.5

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

Add '0.25' to each side of the equation.
-0.5x + 0.25 + x2 = -2.5 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -0.5x + x2 = -2.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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