5a^2+8=-41a

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Solution for 5a^2+8=-41a equation:


Simplifying
5a2 + 8 = -41a

Reorder the terms:
8 + 5a2 = -41a

Solving
8 + 5a2 = -41a

Solving for variable 'a'.

Reorder the terms:
8 + 41a + 5a2 = -41a + 41a

Combine like terms: -41a + 41a = 0
8 + 41a + 5a2 = 0

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

Subproblem 1

Set the factor '(8 + a)' equal to zero and attempt to solve: Simplifying 8 + a = 0 Solving 8 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a = 0 + -8 a = 0 + -8 Combine like terms: 0 + -8 = -8 a = -8 Simplifying a = -8

Subproblem 2

Set the factor '(1 + 5a)' equal to zero and attempt to solve: Simplifying 1 + 5a = 0 Solving 1 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5a = 0 + -1 5a = 0 + -1 Combine like terms: 0 + -1 = -1 5a = -1 Divide each side by '5'. a = -0.2 Simplifying a = -0.2

Solution

a = {-8, -0.2}

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