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Simplifying (10 + 2x)(8 + 2x) = 143 Multiply (10 + 2x) * (8 + 2x) (10(8 + 2x) + 2x * (8 + 2x)) = 143 ((8 * 10 + 2x * 10) + 2x * (8 + 2x)) = 143 ((80 + 20x) + 2x * (8 + 2x)) = 143 (80 + 20x + (8 * 2x + 2x * 2x)) = 143 (80 + 20x + (16x + 4x2)) = 143 Combine like terms: 20x + 16x = 36x (80 + 36x + 4x2) = 143 Solving 80 + 36x + 4x2 = 143 Solving for variable 'x'. Reorder the terms: 80 + -143 + 36x + 4x2 = 143 + -143 Combine like terms: 80 + -143 = -63 -63 + 36x + 4x2 = 143 + -143 Combine like terms: 143 + -143 = 0 -63 + 36x + 4x2 = 0 Factor a trinomial. (-21 + -2x)(3 + -2x) = 0Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve: Simplifying -21 + -2x = 0 Solving -21 + -2x = 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 + -2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2x = 0 + 21 -2x = 0 + 21 Combine like terms: 0 + 21 = 21 -2x = 21 Divide each side by '-2'. x = -10.5 Simplifying x = -10.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-10.5, 1.5}
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