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Simplifying 12x2 + -204x + 630 = 0 Reorder the terms: 630 + -204x + 12x2 = 0 Solving 630 + -204x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(105 + -34x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(105 + -34x + 2x2)' equal to zero and attempt to solve: Simplifying 105 + -34x + 2x2 = 0 Solving 105 + -34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 52.5 + -17x + x2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + -17x + -52.5 + x2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + -17x + x2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + -17x + x2 = 0 + -52.5 -17x + x2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 -17x + x2 = -52.5 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 = -52.5 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -52.5 + 72.25 Combine like terms: -52.5 + 72.25 = 19.75 72.25 + -17x + x2 = 19.75 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -8.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -8.5 = 4.444097209 Simplifying x + -8.5 = 4.444097209 Reorder the terms: -8.5 + x = 4.444097209 Solving -8.5 + x = 4.444097209 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 = 4.444097209 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.444097209 + 8.5 x = 4.444097209 + 8.5 Combine like terms: 4.444097209 + 8.5 = 12.944097209 x = 12.944097209 Simplifying x = 12.944097209Subproblem 2
x + -8.5 = -4.444097209 Simplifying x + -8.5 = -4.444097209 Reorder the terms: -8.5 + x = -4.444097209 Solving -8.5 + x = -4.444097209 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 = -4.444097209 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.444097209 + 8.5 x = -4.444097209 + 8.5 Combine like terms: -4.444097209 + 8.5 = 4.055902791 x = 4.055902791 Simplifying x = 4.055902791Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.944097209, 4.055902791}Solution
x = {12.944097209, 4.055902791}
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