-x^2+6-8=3x+7

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Solution for -x^2+6-8=3x+7 equation:


Simplifying
-1x2 + 6 + -8 = 3x + 7

Reorder the terms:
6 + -8 + -1x2 = 3x + 7

Combine like terms: 6 + -8 = -2
-2 + -1x2 = 3x + 7

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

Solving
-2 + -1x2 = 7 + 3x

Solving for variable 'x'.

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

Combine like terms: -2 + -7 = -9
-9 + -3x + -1x2 = 7 + 3x + -7 + -3x

Reorder the terms:
-9 + -3x + -1x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
-9 + -3x + -1x2 = 0 + 3x + -3x
-9 + -3x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(9 + 3x + x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + x2 = 0 Solving 9 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 3x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 3x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 3x + x2 = 0 + -9 3x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 3x + x2 = -9 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -9 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + 3x + x2 = -6.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -6.75 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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