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Simplifying 49 + -1x2 + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x) Multiply (14 + -1x) * (7 + -2x) 49 + -1x2 + (14(7 + -2x) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x) 49 + -1x2 + ((7 * 14 + -2x * 14) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x) 49 + -1x2 + ((98 + -28x) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x) 49 + -1x2 + (98 + -28x + (7 * -1x + -2x * -1x)) = (21 + -1x)(7 + -3x) 49 + -1x2 + (98 + -28x + (-7x + 2x2)) = (21 + -1x)(7 + -3x) Combine like terms: -28x + -7x = -35x 49 + -1x2 + (98 + -35x + 2x2) = (21 + -1x)(7 + -3x) Reorder the terms: 49 + 98 + -35x + -1x2 + 2x2 = (21 + -1x)(7 + -3x) Combine like terms: 49 + 98 = 147 147 + -35x + -1x2 + 2x2 = (21 + -1x)(7 + -3x) Combine like terms: -1x2 + 2x2 = 1x2 147 + -35x + 1x2 = (21 + -1x)(7 + -3x) Multiply (21 + -1x) * (7 + -3x) 147 + -35x + 1x2 = (21(7 + -3x) + -1x * (7 + -3x)) 147 + -35x + 1x2 = ((7 * 21 + -3x * 21) + -1x * (7 + -3x)) 147 + -35x + 1x2 = ((147 + -63x) + -1x * (7 + -3x)) 147 + -35x + 1x2 = (147 + -63x + (7 * -1x + -3x * -1x)) 147 + -35x + 1x2 = (147 + -63x + (-7x + 3x2)) Combine like terms: -63x + -7x = -70x 147 + -35x + 1x2 = (147 + -70x + 3x2) Add '-147' to each side of the equation. 147 + -35x + -147 + 1x2 = 147 + -70x + -147 + 3x2 Reorder the terms: 147 + -147 + -35x + 1x2 = 147 + -70x + -147 + 3x2 Combine like terms: 147 + -147 = 0 0 + -35x + 1x2 = 147 + -70x + -147 + 3x2 -35x + 1x2 = 147 + -70x + -147 + 3x2 Reorder the terms: -35x + 1x2 = 147 + -147 + -70x + 3x2 Combine like terms: 147 + -147 = 0 -35x + 1x2 = 0 + -70x + 3x2 -35x + 1x2 = -70x + 3x2 Solving -35x + 1x2 = -70x + 3x2 Solving for variable 'x'. Reorder the terms: -35x + 70x + 1x2 + -3x2 = -70x + 3x2 + 70x + -3x2 Combine like terms: -35x + 70x = 35x 35x + 1x2 + -3x2 = -70x + 3x2 + 70x + -3x2 Combine like terms: 1x2 + -3x2 = -2x2 35x + -2x2 = -70x + 3x2 + 70x + -3x2 Reorder the terms: 35x + -2x2 = -70x + 70x + 3x2 + -3x2 Combine like terms: -70x + 70x = 0 35x + -2x2 = 0 + 3x2 + -3x2 35x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 35x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(35 + -2x) = 0Subproblem 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 '(35 + -2x)' equal to zero and attempt to solve: Simplifying 35 + -2x = 0 Solving 35 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -2x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -2x = 0 + -35 -2x = 0 + -35 Combine like terms: 0 + -35 = -35 -2x = -35 Divide each side by '-2'. x = 17.5 Simplifying x = 17.5Solution
x = {0, 17.5}
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