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Simplifying 4x2 + 40x + 75 = 375 Reorder the terms: 75 + 40x + 4x2 = 375 Solving 75 + 40x + 4x2 = 375 Solving for variable 'x'. Reorder the terms: 75 + -375 + 40x + 4x2 = 375 + -375 Combine like terms: 75 + -375 = -300 -300 + 40x + 4x2 = 375 + -375 Combine like terms: 375 + -375 = 0 -300 + 40x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + 10x + x2) = 0 Factor a trinomial. 4((-15 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 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 = {-15, 5}
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