16x^2+32x+61=81

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Solution for 16x^2+32x+61=81 equation:


Simplifying
16x2 + 32x + 61 = 81

Reorder the terms:
61 + 32x + 16x2 = 81

Solving
61 + 32x + 16x2 = 81

Solving for variable 'x'.

Reorder the terms:
61 + -81 + 32x + 16x2 = 81 + -81

Combine like terms: 61 + -81 = -20
-20 + 32x + 16x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-20 + 32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 8x + 4x2) = 0

Factor a trinomial.
4((-5 + -2x)(1 + -2x)) = 0

Ignore the factor 4.

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 '(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 = {-2.5, 0.5}

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