-1(x)=4x^2-5x+10

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Solution for -1(x)=4x^2-5x+10 equation: 


Simplifying
-1(x) = 4x2 + -5x + 10

Reorder the terms:
-1x = 10 + -5x + 4x2

Solving
-1x = 10 + -5x + 4x2

Solving for variable 'x'.

Reorder the terms:
-10 + -1x + 5x + -4x2 = 10 + -5x + 4x2 + -10 + 5x + -4x2

Combine like terms: -1x + 5x = 4x
-10 + 4x + -4x2 = 10 + -5x + 4x2 + -10 + 5x + -4x2

Reorder the terms:
-10 + 4x + -4x2 = 10 + -10 + -5x + 5x + 4x2 + -4x2

Combine like terms: 10 + -10 = 0
-10 + 4x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
-10 + 4x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
-10 + 4x + -4x2 = 0 + 4x2 + -4x2
-10 + 4x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-10 + 4x + -4x2 = 0

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

Ignore the factor 2.

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

Simplifying
-5 + 2x + -2x2 = 0

Solving
-5 + 2x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1x + x2 = 0 + -2.5
-1x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1x + x2 = -2.5

The x term is -1x.  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.
-1x + 0.25 + x2 = -2.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -1x + 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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