-x^2=7x+10

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Solution for -x^2=7x+10 equation:


Simplifying
-1x2 = 7x + 10

Reorder the terms:
-1x2 = 10 + 7x

Solving
-1x2 = 10 + 7x

Solving for variable 'x'.

Reorder the terms:
-10 + -7x + -1x2 = 10 + 7x + -10 + -7x

Reorder the terms:
-10 + -7x + -1x2 = 10 + -10 + 7x + -7x

Combine like terms: 10 + -10 = 0
-10 + -7x + -1x2 = 0 + 7x + -7x
-10 + -7x + -1x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-10 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 7x + x2) = 0

Factor a trinomial.
-1((5 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-5, -2}

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