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Simplifying 12x2 + -216x + 585 = 0 Reorder the terms: 585 + -216x + 12x2 = 0 Solving 585 + -216x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(195 + -72x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(195 + -72x + 4x2)' equal to zero and attempt to solve: Simplifying 195 + -72x + 4x2 = 0 Solving 195 + -72x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 48.75 + -18x + x2 = 0 Move the constant term to the right: Add '-48.75' to each side of the equation. 48.75 + -18x + -48.75 + x2 = 0 + -48.75 Reorder the terms: 48.75 + -48.75 + -18x + x2 = 0 + -48.75 Combine like terms: 48.75 + -48.75 = 0.00 0.00 + -18x + x2 = 0 + -48.75 -18x + x2 = 0 + -48.75 Combine like terms: 0 + -48.75 = -48.75 -18x + x2 = -48.75 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -48.75 + 81 Reorder the terms: 81 + -18x + x2 = -48.75 + 81 Combine like terms: -48.75 + 81 = 32.25 81 + -18x + x2 = 32.25 Factor a perfect square on the left side: (x + -9)(x + -9) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -9) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -9 = 5.678908346 Simplifying x + -9 = 5.678908346 Reorder the terms: -9 + x = 5.678908346 Solving -9 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 5.678908346 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.678908346 + 9 x = 5.678908346 + 9 Combine like terms: 5.678908346 + 9 = 14.678908346 x = 14.678908346 Simplifying x = 14.678908346Subproblem 2
x + -9 = -5.678908346 Simplifying x + -9 = -5.678908346 Reorder the terms: -9 + x = -5.678908346 Solving -9 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -5.678908346 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.678908346 + 9 x = -5.678908346 + 9 Combine like terms: -5.678908346 + 9 = 3.321091654 x = 3.321091654 Simplifying x = 3.321091654Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.678908346, 3.321091654}Solution
x = {14.678908346, 3.321091654}
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