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Simplifying 3x2 + 75 = 4x2 + 10x Reorder the terms: 75 + 3x2 = 4x2 + 10x Reorder the terms: 75 + 3x2 = 10x + 4x2 Solving 75 + 3x2 = 10x + 4x2 Solving for variable 'x'. Reorder the terms: 75 + -10x + 3x2 + -4x2 = 10x + 4x2 + -10x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 75 + -10x + -1x2 = 10x + 4x2 + -10x + -4x2 Reorder the terms: 75 + -10x + -1x2 = 10x + -10x + 4x2 + -4x2 Combine like terms: 10x + -10x = 0 75 + -10x + -1x2 = 0 + 4x2 + -4x2 75 + -10x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 75 + -10x + -1x2 = 0 Factor a trinomial. (5 + -1x)(15 + x) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 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 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {5, -15}
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