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Simplifying (30 + -2x)(17 + -2x) = 510 Multiply (30 + -2x) * (17 + -2x) (30(17 + -2x) + -2x * (17 + -2x)) = 510 ((17 * 30 + -2x * 30) + -2x * (17 + -2x)) = 510 ((510 + -60x) + -2x * (17 + -2x)) = 510 (510 + -60x + (17 * -2x + -2x * -2x)) = 510 (510 + -60x + (-34x + 4x2)) = 510 Combine like terms: -60x + -34x = -94x (510 + -94x + 4x2) = 510 Add '-510' to each side of the equation. 510 + -94x + -510 + 4x2 = 510 + -510 Reorder the terms: 510 + -510 + -94x + 4x2 = 510 + -510 Combine like terms: 510 + -510 = 0 0 + -94x + 4x2 = 510 + -510 -94x + 4x2 = 510 + -510 Combine like terms: 510 + -510 = 0 -94x + 4x2 = 0 Solving -94x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-47 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-47 + 2x)' equal to zero and attempt to solve: Simplifying -47 + 2x = 0 Solving -47 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + 2x = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2x = 0 + 47 2x = 0 + 47 Combine like terms: 0 + 47 = 47 2x = 47 Divide each side by '2'. x = 23.5 Simplifying x = 23.5Solution
x = {0, 23.5}
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