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Simplifying 3965 = -10x2 + 265x + 2600 Reorder the terms: 3965 = 2600 + 265x + -10x2 Solving 3965 = 2600 + 265x + -10x2 Solving for variable 'x'. Combine like terms: 3965 + -2600 = 1365 1365 + -265x + 10x2 = 2600 + 265x + -10x2 + -2600 + -265x + 10x2 Reorder the terms: 1365 + -265x + 10x2 = 2600 + -2600 + 265x + -265x + -10x2 + 10x2 Combine like terms: 2600 + -2600 = 0 1365 + -265x + 10x2 = 0 + 265x + -265x + -10x2 + 10x2 1365 + -265x + 10x2 = 265x + -265x + -10x2 + 10x2 Combine like terms: 265x + -265x = 0 1365 + -265x + 10x2 = 0 + -10x2 + 10x2 1365 + -265x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 1365 + -265x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(273 + -53x + 2x2) = 0 Factor a trinomial. 5((7 + -1x)(39 + -2x)) = 0 Ignore the factor 5.Subproblem 1
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 = 7Subproblem 2
Set the factor '(39 + -2x)' equal to zero and attempt to solve: Simplifying 39 + -2x = 0 Solving 39 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + -2x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -2x = 0 + -39 -2x = 0 + -39 Combine like terms: 0 + -39 = -39 -2x = -39 Divide each side by '-2'. x = 19.5 Simplifying x = 19.5Solution
x = {7, 19.5}
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