5x^2=-7x-2

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Solution for 5x^2=-7x-2 equation:


Simplifying
5x2 = -7x + -2

Reorder the terms:
5x2 = -2 + -7x

Solving
5x2 = -2 + -7x

Solving for variable 'x'.

Reorder the terms:
2 + 7x + 5x2 = -2 + -7x + 2 + 7x

Reorder the terms:
2 + 7x + 5x2 = -2 + 2 + -7x + 7x

Combine like terms: -2 + 2 = 0
2 + 7x + 5x2 = 0 + -7x + 7x
2 + 7x + 5x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
2 + 7x + 5x2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4

Solution

x = {-1, -0.4}

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