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Simplifying 0 = 8x2 + -42x + 45 Reorder the terms: 0 = 45 + -42x + 8x2 Solving 0 = 45 + -42x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + 42x + -8x2 = 45 + -42x + 8x2 + -45 + 42x + -8x2 Reorder the terms: -45 + 42x + -8x2 = 45 + -45 + -42x + 42x + 8x2 + -8x2 Combine like terms: 45 + -45 = 0 -45 + 42x + -8x2 = 0 + -42x + 42x + 8x2 + -8x2 -45 + 42x + -8x2 = -42x + 42x + 8x2 + -8x2 Combine like terms: -42x + 42x = 0 -45 + 42x + -8x2 = 0 + 8x2 + -8x2 -45 + 42x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -45 + 42x + -8x2 = 0 Factor a trinomial. (-15 + 4x)(3 + -2x) = 0Subproblem 1
Set the factor '(-15 + 4x)' equal to zero and attempt to solve: Simplifying -15 + 4x = 0 Solving -15 + 4x = 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 + 4x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4x = 0 + 15 4x = 0 + 15 Combine like terms: 0 + 15 = 15 4x = 15 Divide each side by '4'. x = 3.75 Simplifying x = 3.75Subproblem 2
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 = 1.5Solution
x = {3.75, 1.5}
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