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Simplifying 6x2 + -6x + 10 = 2x2 + -2x + 25 Reorder the terms: 10 + -6x + 6x2 = 2x2 + -2x + 25 Reorder the terms: 10 + -6x + 6x2 = 25 + -2x + 2x2 Solving 10 + -6x + 6x2 = 25 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: 10 + -25 + -6x + 2x + 6x2 + -2x2 = 25 + -2x + 2x2 + -25 + 2x + -2x2 Combine like terms: 10 + -25 = -15 -15 + -6x + 2x + 6x2 + -2x2 = 25 + -2x + 2x2 + -25 + 2x + -2x2 Combine like terms: -6x + 2x = -4x -15 + -4x + 6x2 + -2x2 = 25 + -2x + 2x2 + -25 + 2x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 -15 + -4x + 4x2 = 25 + -2x + 2x2 + -25 + 2x + -2x2 Reorder the terms: -15 + -4x + 4x2 = 25 + -25 + -2x + 2x + 2x2 + -2x2 Combine like terms: 25 + -25 = 0 -15 + -4x + 4x2 = 0 + -2x + 2x + 2x2 + -2x2 -15 + -4x + 4x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -15 + -4x + 4x2 = 0 + 2x2 + -2x2 -15 + -4x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -4x + 4x2 = 0 Factor a trinomial. (-3 + -2x)(5 + -2x) = 0Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-1.5, 2.5}
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