(8+x)(10+x)=224

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Solution for (8+x)(10+x)=224 equation:


Simplifying
(8 + x)(10 + x) = 224

Multiply (8 + x) * (10 + x)
(8(10 + x) + x(10 + x)) = 224
((10 * 8 + x * 8) + x(10 + x)) = 224
((80 + 8x) + x(10 + x)) = 224
(80 + 8x + (10 * x + x * x)) = 224
(80 + 8x + (10x + x2)) = 224

Combine like terms: 8x + 10x = 18x
(80 + 18x + x2) = 224

Solving
80 + 18x + x2 = 224

Solving for variable 'x'.

Reorder the terms:
80 + -224 + 18x + x2 = 224 + -224

Combine like terms: 80 + -224 = -144
-144 + 18x + x2 = 224 + -224

Combine like terms: 224 + -224 = 0
-144 + 18x + x2 = 0

Factor a trinomial.
(-24 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-24 + -1x)' equal to zero and attempt to solve: Simplifying -24 + -1x = 0 Solving -24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1x = 0 + 24 -1x = 0 + 24 Combine like terms: 0 + 24 = 24 -1x = 24 Divide each side by '-1'. x = -24 Simplifying x = -24

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-24, 6}

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