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Simplifying x2 + (48 + -1x)(64 + -1x) = 1536 Multiply (48 + -1x) * (64 + -1x) x2 + (48(64 + -1x) + -1x * (64 + -1x)) = 1536 x2 + ((64 * 48 + -1x * 48) + -1x * (64 + -1x)) = 1536 x2 + ((3072 + -48x) + -1x * (64 + -1x)) = 1536 x2 + (3072 + -48x + (64 * -1x + -1x * -1x)) = 1536 x2 + (3072 + -48x + (-64x + 1x2)) = 1536 Combine like terms: -48x + -64x = -112x x2 + (3072 + -112x + 1x2) = 1536 Reorder the terms: 3072 + -112x + x2 + 1x2 = 1536 Combine like terms: x2 + 1x2 = 2x2 3072 + -112x + 2x2 = 1536 Solving 3072 + -112x + 2x2 = 1536 Solving for variable 'x'. Reorder the terms: 3072 + -1536 + -112x + 2x2 = 1536 + -1536 Combine like terms: 3072 + -1536 = 1536 1536 + -112x + 2x2 = 1536 + -1536 Combine like terms: 1536 + -1536 = 0 1536 + -112x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(768 + -56x + x2) = 0 Factor a trinomial. 2((24 + -1x)(32 + -1x)) = 0 Ignore the factor 2.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 = 24Subproblem 2
Set the factor '(32 + -1x)' equal to zero and attempt to solve: Simplifying 32 + -1x = 0 Solving 32 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -1x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 0 + -32 -1x = 0 + -32 Combine like terms: 0 + -32 = -32 -1x = -32 Divide each side by '-1'. x = 32 Simplifying x = 32Solution
x = {24, 32}
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