2x^2=-9x-10

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Solution for 2x^2=-9x-10 equation:


Simplifying
2x2 = -9x + -10

Reorder the terms:
2x2 = -10 + -9x

Solving
2x2 = -10 + -9x

Solving for variable 'x'.

Reorder the terms:
10 + 9x + 2x2 = -10 + -9x + 10 + 9x

Reorder the terms:
10 + 9x + 2x2 = -10 + 10 + -9x + 9x

Combine like terms: -10 + 10 = 0
10 + 9x + 2x2 = 0 + -9x + 9x
10 + 9x + 2x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
10 + 9x + 2x2 = 0

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

Subproblem 1

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

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 = {-2.5, -2}

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