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Simplifying 7x(x + -4) + x = 8(x + -4) + 4 Reorder the terms: 7x(-4 + x) + x = 8(x + -4) + 4 (-4 * 7x + x * 7x) + x = 8(x + -4) + 4 (-28x + 7x2) + x = 8(x + -4) + 4 Reorder the terms: -28x + x + 7x2 = 8(x + -4) + 4 Combine like terms: -28x + x = -27x -27x + 7x2 = 8(x + -4) + 4 Reorder the terms: -27x + 7x2 = 8(-4 + x) + 4 -27x + 7x2 = (-4 * 8 + x * 8) + 4 -27x + 7x2 = (-32 + 8x) + 4 Reorder the terms: -27x + 7x2 = -32 + 4 + 8x Combine like terms: -32 + 4 = -28 -27x + 7x2 = -28 + 8x Solving -27x + 7x2 = -28 + 8x Solving for variable 'x'. Reorder the terms: 28 + -27x + -8x + 7x2 = -28 + 8x + 28 + -8x Combine like terms: -27x + -8x = -35x 28 + -35x + 7x2 = -28 + 8x + 28 + -8x Reorder the terms: 28 + -35x + 7x2 = -28 + 28 + 8x + -8x Combine like terms: -28 + 28 = 0 28 + -35x + 7x2 = 0 + 8x + -8x 28 + -35x + 7x2 = 8x + -8x Combine like terms: 8x + -8x = 0 28 + -35x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(4 + -5x + x2) = 0 Factor a trinomial. 7((1 + -1x)(4 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {1, 4}
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