x^2+2x=2x^2-35

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Solution for x^2+2x=2x^2-35 equation:


Simplifying
x2 + 2x = 2x2 + -35

Reorder the terms:
2x + x2 = 2x2 + -35

Reorder the terms:
2x + x2 = -35 + 2x2

Solving
2x + x2 = -35 + 2x2

Solving for variable 'x'.

Reorder the terms:
35 + 2x + x2 + -2x2 = -35 + 2x2 + 35 + -2x2

Combine like terms: x2 + -2x2 = -1x2
35 + 2x + -1x2 = -35 + 2x2 + 35 + -2x2

Reorder the terms:
35 + 2x + -1x2 = -35 + 35 + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
35 + 2x + -1x2 = 0 + 2x2 + -2x2
35 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
35 + 2x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(5 + x) = 0

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

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 = {7, -5}

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