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Simplifying -3x2 + 66x + -60 = 0 Reorder the terms: -60 + 66x + -3x2 = 0 Solving -60 + 66x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + 22x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-20 + 22x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 22x + -1x2 = 0 Solving -20 + 22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -22x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -22x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -22x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -22x + x2 = 0 + -20 -22x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -22x + x2 = -20 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -20 + 121 Reorder the terms: 121 + -22x + x2 = -20 + 121 Combine like terms: -20 + 121 = 101 121 + -22x + x2 = 101 Factor a perfect square on the left side: (x + -11)(x + -11) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -11) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -11 = 10.049875621 Simplifying x + -11 = 10.049875621 Reorder the terms: -11 + x = 10.049875621 Solving -11 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.049875621 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.049875621 + 11 x = 10.049875621 + 11 Combine like terms: 10.049875621 + 11 = 21.049875621 x = 21.049875621 Simplifying x = 21.049875621Subproblem 2
x + -11 = -10.049875621 Simplifying x + -11 = -10.049875621 Reorder the terms: -11 + x = -10.049875621 Solving -11 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.049875621 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.049875621 + 11 x = -10.049875621 + 11 Combine like terms: -10.049875621 + 11 = 0.950124379 x = 0.950124379 Simplifying x = 0.950124379Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.049875621, 0.950124379}Solution
x = {21.049875621, 0.950124379}
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