-11x-45=3+x^2-6x-7

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Solution for -11x-45=3+x^2-6x-7 equation:


Simplifying
-11x + -45 = 3 + x2 + -6x + -7

Reorder the terms:
-45 + -11x = 3 + x2 + -6x + -7

Reorder the terms:
-45 + -11x = 3 + -7 + -6x + x2

Combine like terms: 3 + -7 = -4
-45 + -11x = -4 + -6x + x2

Solving
-45 + -11x = -4 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-45 + 4 + -11x + 6x + -1x2 = -4 + -6x + x2 + 4 + 6x + -1x2

Combine like terms: -45 + 4 = -41
-41 + -11x + 6x + -1x2 = -4 + -6x + x2 + 4 + 6x + -1x2

Combine like terms: -11x + 6x = -5x
-41 + -5x + -1x2 = -4 + -6x + x2 + 4 + 6x + -1x2

Reorder the terms:
-41 + -5x + -1x2 = -4 + 4 + -6x + 6x + x2 + -1x2

Combine like terms: -4 + 4 = 0
-41 + -5x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-41 + -5x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-41 + -5x + -1x2 = 0 + x2 + -1x2
-41 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-41 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(41 + 5x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(41 + 5x + x2)' equal to zero and attempt to solve: Simplifying 41 + 5x + x2 = 0 Solving 41 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 5x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 5x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 5x + x2 = 0 + -41 5x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 5x + x2 = -41 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -41 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -41 + 6.25 Combine like terms: -41 + 6.25 = -34.75 6.25 + 5x + x2 = -34.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -34.75 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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