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Simplifying 81 + -90x + 25x2 = x2 Solving 81 + -90x + 25x2 = x2 Solving for variable 'x'. Combine like terms: 25x2 + -1x2 = 24x2 81 + -90x + 24x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -90x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -30x + 8x2) = 0 Factor a trinomial. 3((3 + -2x)(9 + -4x)) = 0 Ignore the factor 3.Subproblem 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 '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {1.5, 2.25}
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