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Simplifying (x + -10)(4x + 1) = x + -110 Reorder the terms: (-10 + x)(4x + 1) = x + -110 Reorder the terms: (-10 + x)(1 + 4x) = x + -110 Multiply (-10 + x) * (1 + 4x) (-10(1 + 4x) + x(1 + 4x)) = x + -110 ((1 * -10 + 4x * -10) + x(1 + 4x)) = x + -110 ((-10 + -40x) + x(1 + 4x)) = x + -110 (-10 + -40x + (1 * x + 4x * x)) = x + -110 (-10 + -40x + (1x + 4x2)) = x + -110 Combine like terms: -40x + 1x = -39x (-10 + -39x + 4x2) = x + -110 Reorder the terms: -10 + -39x + 4x2 = -110 + x Solving -10 + -39x + 4x2 = -110 + x Solving for variable 'x'. Reorder the terms: -10 + 110 + -39x + -1x + 4x2 = -110 + x + 110 + -1x Combine like terms: -10 + 110 = 100 100 + -39x + -1x + 4x2 = -110 + x + 110 + -1x Combine like terms: -39x + -1x = -40x 100 + -40x + 4x2 = -110 + x + 110 + -1x Reorder the terms: 100 + -40x + 4x2 = -110 + 110 + x + -1x Combine like terms: -110 + 110 = 0 100 + -40x + 4x2 = 0 + x + -1x 100 + -40x + 4x2 = x + -1x Combine like terms: x + -1x = 0 100 + -40x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -10x + x2) = 0 Factor a trinomial. 4((5 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5, 5}
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