-a^2-10a=25

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Solution for -a^2-10a=25 equation:


Simplifying
-1a2 + -10a = 25

Reorder the terms:
-10a + -1a2 = 25

Solving
-10a + -1a2 = 25

Solving for variable 'a'.

Reorder the terms:
-25 + -10a + -1a2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -10a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 10a + a2) = 0

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

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

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

Solution

a = {-5, -5}

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