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Simplifying x2 + 4x2 + 40x + 100 = 625 Reorder the terms: 100 + 40x + x2 + 4x2 = 625 Combine like terms: x2 + 4x2 = 5x2 100 + 40x + 5x2 = 625 Solving 100 + 40x + 5x2 = 625 Solving for variable 'x'. Reorder the terms: 100 + -625 + 40x + 5x2 = 625 + -625 Combine like terms: 100 + -625 = -525 -525 + 40x + 5x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -525 + 40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-105 + 8x + x2) = 0 Factor a trinomial. 5((-15 + -1x)(7 + -1x)) = 0 Ignore the factor 5.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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-15, 7}
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