10=x^2+2x-5

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Solution for 10=x^2+2x-5 equation:


Simplifying
10 = x2 + 2x + -5

Reorder the terms:
10 = -5 + 2x + x2

Solving
10 = -5 + 2x + x2

Solving for variable 'x'.

Combine like terms: 10 + 5 = 15
15 + -2x + -1x2 = -5 + 2x + x2 + 5 + -2x + -1x2

Reorder the terms:
15 + -2x + -1x2 = -5 + 5 + 2x + -2x + x2 + -1x2

Combine like terms: -5 + 5 = 0
15 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
15 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
15 + -2x + -1x2 = 0 + x2 + -1x2
15 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -2x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(5 + x) = 0

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {3, -5}

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