(-x^2+4x-3)-(5x^2+2x+7)=

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Solution for (-x^2+4x-3)-(5x^2+2x+7)= equation: 


Simplifying
(-1x2 + 4x + -3) + -1(5x2 + 2x + 7) = 0

Reorder the terms:
(-3 + 4x + -1x2) + -1(5x2 + 2x + 7) = 0

Remove parenthesis around (-3 + 4x + -1x2)
-3 + 4x + -1x2 + -1(5x2 + 2x + 7) = 0

Reorder the terms:
-3 + 4x + -1x2 + -1(7 + 2x + 5x2) = 0
-3 + 4x + -1x2 + (7 * -1 + 2x * -1 + 5x2 * -1) = 0
-3 + 4x + -1x2 + (-7 + -2x + -5x2) = 0

Reorder the terms:
-3 + -7 + 4x + -2x + -1x2 + -5x2 = 0

Combine like terms: -3 + -7 = -10
-10 + 4x + -2x + -1x2 + -5x2 = 0

Combine like terms: 4x + -2x = 2x
-10 + 2x + -1x2 + -5x2 = 0

Combine like terms: -1x2 + -5x2 = -6x2
-10 + 2x + -6x2 = 0

Solving
-10 + 2x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + x + -3x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + -3x2 = 0

Solving
-5 + x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -0.3333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -0.3333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + -1.666666667
-0.3333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-0.3333333333x + x2 = -1.666666667

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.
-0.3333333333x + 0.25 + x2 = -1.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = -1.666666667 + 0.25

Combine like terms: -1.666666667 + 0.25 = -1.416666667
0.25 + -0.3333333333x + x2 = -1.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.416666667

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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