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Simplifying 4x(x + 4) = 10(x + 1) Reorder the terms: 4x(4 + x) = 10(x + 1) (4 * 4x + x * 4x) = 10(x + 1) (16x + 4x2) = 10(x + 1) Reorder the terms: 16x + 4x2 = 10(1 + x) 16x + 4x2 = (1 * 10 + x * 10) 16x + 4x2 = (10 + 10x) Solving 16x + 4x2 = 10 + 10x Solving for variable 'x'. Reorder the terms: -10 + 16x + -10x + 4x2 = 10 + 10x + -10 + -10x Combine like terms: 16x + -10x = 6x -10 + 6x + 4x2 = 10 + 10x + -10 + -10x Reorder the terms: -10 + 6x + 4x2 = 10 + -10 + 10x + -10x Combine like terms: 10 + -10 = 0 -10 + 6x + 4x2 = 0 + 10x + -10x -10 + 6x + 4x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -10 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 3x + 2x2) = 0 Factor a trinomial. 2((-5 + -2x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
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 = 1Solution
x = {-2.5, 1}
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