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Simplifying 4x2 + 380x + 8400 = 15000 Reorder the terms: 8400 + 380x + 4x2 = 15000 Solving 8400 + 380x + 4x2 = 15000 Solving for variable 'x'. Reorder the terms: 8400 + -15000 + 380x + 4x2 = 15000 + -15000 Combine like terms: 8400 + -15000 = -6600 -6600 + 380x + 4x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 -6600 + 380x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1650 + 95x + x2) = 0 Factor a trinomial. 4((-110 + -1x)(15 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-110 + -1x)' equal to zero and attempt to solve: Simplifying -110 + -1x = 0 Solving -110 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + -1x = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -1x = 0 + 110 -1x = 0 + 110 Combine like terms: 0 + 110 = 110 -1x = 110 Divide each side by '-1'. x = -110 Simplifying x = -110Subproblem 2
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 = 15Solution
x = {-110, 15}
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