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Simplifying 6x2 + -20 = 15x + 1 Reorder the terms: -20 + 6x2 = 15x + 1 Reorder the terms: -20 + 6x2 = 1 + 15x Solving -20 + 6x2 = 1 + 15x Solving for variable 'x'. Reorder the terms: -20 + -1 + -15x + 6x2 = 1 + 15x + -1 + -15x Combine like terms: -20 + -1 = -21 -21 + -15x + 6x2 = 1 + 15x + -1 + -15x Reorder the terms: -21 + -15x + 6x2 = 1 + -1 + 15x + -15x Combine like terms: 1 + -1 = 0 -21 + -15x + 6x2 = 0 + 15x + -15x -21 + -15x + 6x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -21 + -15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -5x + 2x2) = 0 Factor a trinomial. 3((-1 + -1x)(7 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {-1, 3.5}
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