-2x^2=9x+4

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Solution for -2x^2=9x+4 equation:


Simplifying
-2x2 = 9x + 4

Reorder the terms:
-2x2 = 4 + 9x

Solving
-2x2 = 4 + 9x

Solving for variable 'x'.

Reorder the terms:
-4 + -9x + -2x2 = 4 + 9x + -4 + -9x

Reorder the terms:
-4 + -9x + -2x2 = 4 + -4 + 9x + -9x

Combine like terms: 4 + -4 = 0
-4 + -9x + -2x2 = 0 + 9x + -9x
-4 + -9x + -2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-4 + -9x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 9x + 2x2) = 0

Factor a trinomial.
-1((4 + x)(1 + 2x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-4, -0.5}

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