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Simplifying 51x = 24x2 + 6 Reorder the terms: 51x = 6 + 24x2 Solving 51x = 6 + 24x2 Solving for variable 'x'. Reorder the terms: -6 + 51x + -24x2 = 6 + 24x2 + -6 + -24x2 Reorder the terms: -6 + 51x + -24x2 = 6 + -6 + 24x2 + -24x2 Combine like terms: 6 + -6 = 0 -6 + 51x + -24x2 = 0 + 24x2 + -24x2 -6 + 51x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -6 + 51x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 17x + -8x2) = 0 Factor a trinomial. 3((-2 + x)(1 + -8x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 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 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125Solution
x = {2, 0.125}
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