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Simplifying 4x2 + 204x + 2601 = x2 + 41616 Reorder the terms: 2601 + 204x + 4x2 = x2 + 41616 Reorder the terms: 2601 + 204x + 4x2 = 41616 + x2 Solving 2601 + 204x + 4x2 = 41616 + x2 Solving for variable 'x'. Reorder the terms: 2601 + -41616 + 204x + 4x2 + -1x2 = 41616 + x2 + -41616 + -1x2 Combine like terms: 2601 + -41616 = -39015 -39015 + 204x + 4x2 + -1x2 = 41616 + x2 + -41616 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -39015 + 204x + 3x2 = 41616 + x2 + -41616 + -1x2 Reorder the terms: -39015 + 204x + 3x2 = 41616 + -41616 + x2 + -1x2 Combine like terms: 41616 + -41616 = 0 -39015 + 204x + 3x2 = 0 + x2 + -1x2 -39015 + 204x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -39015 + 204x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13005 + 68x + x2) = 0 Factor a trinomial. 3((-153 + -1x)(85 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-153 + -1x)' equal to zero and attempt to solve: Simplifying -153 + -1x = 0 Solving -153 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '153' to each side of the equation. -153 + 153 + -1x = 0 + 153 Combine like terms: -153 + 153 = 0 0 + -1x = 0 + 153 -1x = 0 + 153 Combine like terms: 0 + 153 = 153 -1x = 153 Divide each side by '-1'. x = -153 Simplifying x = -153Subproblem 2
Set the factor '(85 + -1x)' equal to zero and attempt to solve: Simplifying 85 + -1x = 0 Solving 85 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-85' to each side of the equation. 85 + -85 + -1x = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -1x = 0 + -85 -1x = 0 + -85 Combine like terms: 0 + -85 = -85 -1x = -85 Divide each side by '-1'. x = 85 Simplifying x = 85Solution
x = {-153, 85}
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