x^2-16=9-24x

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Solution for x^2-16=9-24x equation:


Simplifying
x2 + -16 = 9 + -24x

Reorder the terms:
-16 + x2 = 9 + -24x

Solving
-16 + x2 = 9 + -24x

Solving for variable 'x'.

Reorder the terms:
-16 + -9 + 24x + x2 = 9 + -24x + -9 + 24x

Combine like terms: -16 + -9 = -25
-25 + 24x + x2 = 9 + -24x + -9 + 24x

Reorder the terms:
-25 + 24x + x2 = 9 + -9 + -24x + 24x

Combine like terms: 9 + -9 = 0
-25 + 24x + x2 = 0 + -24x + 24x
-25 + 24x + x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-25 + 24x + x2 = 0

Factor a trinomial.
(-25 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-25 + -1x)' equal to zero and attempt to solve: Simplifying -25 + -1x = 0 Solving -25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x = 0 + 25 -1x = 0 + 25 Combine like terms: 0 + 25 = 25 -1x = 25 Divide each side by '-1'. x = -25 Simplifying x = -25

Subproblem 2

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

Solution

x = {-25, 1}

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