(11+x)(16+x)=500

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Solution for (11+x)(16+x)=500 equation:


Simplifying
(11 + x)(16 + x) = 500

Multiply (11 + x) * (16 + x)
(11(16 + x) + x(16 + x)) = 500
((16 * 11 + x * 11) + x(16 + x)) = 500
((176 + 11x) + x(16 + x)) = 500
(176 + 11x + (16 * x + x * x)) = 500
(176 + 11x + (16x + x2)) = 500

Combine like terms: 11x + 16x = 27x
(176 + 27x + x2) = 500

Solving
176 + 27x + x2 = 500

Solving for variable 'x'.

Reorder the terms:
176 + -500 + 27x + x2 = 500 + -500

Combine like terms: 176 + -500 = -324
-324 + 27x + x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-324 + 27x + x2 = 0

Factor a trinomial.
(-36 + -1x)(9 + -1x) = 0

Subproblem 1

Set the factor '(-36 + -1x)' equal to zero and attempt to solve: Simplifying -36 + -1x = 0 Solving -36 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + -1x = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1x = 0 + 36 -1x = 0 + 36 Combine like terms: 0 + 36 = 36 -1x = 36 Divide each side by '-1'. x = -36 Simplifying x = -36

Subproblem 2

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {-36, 9}

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