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Simplifying 12x2 + -204x + -594 = 0 Reorder the terms: -594 + -204x + 12x2 = 0 Solving -594 + -204x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-99 + -34x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-99 + -34x + 2x2)' equal to zero and attempt to solve: Simplifying -99 + -34x + 2x2 = 0 Solving -99 + -34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49.5 + -17x + x2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + -17x + 49.5 + x2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + -17x + x2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + -17x + x2 = 0 + 49.5 -17x + x2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 -17x + x2 = 49.5 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 49.5 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 49.5 + 72.25 Combine like terms: 49.5 + 72.25 = 121.75 72.25 + -17x + x2 = 121.75 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 121.75 Calculate the square root of the right side: 11.034038245 Break this problem into two subproblems by setting (x + -8.5) equal to 11.034038245 and -11.034038245.Subproblem 1
x + -8.5 = 11.034038245 Simplifying x + -8.5 = 11.034038245 Reorder the terms: -8.5 + x = 11.034038245 Solving -8.5 + x = 11.034038245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 11.034038245 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 11.034038245 + 8.5 x = 11.034038245 + 8.5 Combine like terms: 11.034038245 + 8.5 = 19.534038245 x = 19.534038245 Simplifying x = 19.534038245Subproblem 2
x + -8.5 = -11.034038245 Simplifying x + -8.5 = -11.034038245 Reorder the terms: -8.5 + x = -11.034038245 Solving -8.5 + x = -11.034038245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -11.034038245 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -11.034038245 + 8.5 x = -11.034038245 + 8.5 Combine like terms: -11.034038245 + 8.5 = -2.534038245 x = -2.534038245 Simplifying x = -2.534038245Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.534038245, -2.534038245}Solution
x = {19.534038245, -2.534038245}
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