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Simplifying (22 + 2x)(10 + 2x) + -1(22 * 10) = 420 Multiply (22 + 2x) * (10 + 2x) (22(10 + 2x) + 2x * (10 + 2x)) + -1(22 * 10) = 420 ((10 * 22 + 2x * 22) + 2x * (10 + 2x)) + -1(22 * 10) = 420 ((220 + 44x) + 2x * (10 + 2x)) + -1(22 * 10) = 420 (220 + 44x + (10 * 2x + 2x * 2x)) + -1(22 * 10) = 420 (220 + 44x + (20x + 4x2)) + -1(22 * 10) = 420 Combine like terms: 44x + 20x = 64x (220 + 64x + 4x2) + -1(22 * 10) = 420 Multiply 22 * 10 220 + 64x + 4x2 + -1(220) = 420 Multiply -1 * 220 220 + 64x + 4x2 + -220 = 420 Reorder the terms: 220 + -220 + 64x + 4x2 = 420 Combine like terms: 220 + -220 = 0 0 + 64x + 4x2 = 420 64x + 4x2 = 420 Solving 64x + 4x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 64x + 4x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 64x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-105 + 16x + x2) = 0 Factor a trinomial. 4((-21 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-21, 5}
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