x^2+8=-3x+6

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


Simplifying
x2 + 8 = -3x + 6

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

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

Solving
8 + x2 = 6 + -3x

Solving for variable 'x'.

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

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

Reorder the terms:
2 + 3x + x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
2 + 3x + x2 = 0 + -3x + 3x
2 + 3x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
2 + 3x + x2 = 0

Factor a trinomial.
(2 + x)(1 + x) = 0

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-2, -1}

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