-16x^2+80x=100

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Solution for -16x^2+80x=100 equation:


Simplifying
-16x2 + 80x = 100

Reorder the terms:
80x + -16x2 = 100

Solving
80x + -16x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 80x + -16x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 80x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 20x + -4x2) = 0

Factor a trinomial.
4((-5 + 2x)(5 + -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 '(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

Solution

x = {2.5, 2.5}

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