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Simplifying -6x2 + 66x + 60 = 0 Reorder the terms: 60 + 66x + -6x2 = 0 Solving 60 + 66x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(10 + 11x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(10 + 11x + -1x2)' equal to zero and attempt to solve: Simplifying 10 + 11x + -1x2 = 0 Solving 10 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -11x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -11x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -11x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11x + x2 = 0 + 10 -11x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -11x + x2 = 10 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 10 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + -11x + x2 = 40.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -5.5 = 6.34428877 Simplifying x + -5.5 = 6.34428877 Reorder the terms: -5.5 + x = 6.34428877 Solving -5.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.34428877 + 5.5 x = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 x = 11.84428877 Simplifying x = 11.84428877Subproblem 2
x + -5.5 = -6.34428877 Simplifying x + -5.5 = -6.34428877 Reorder the terms: -5.5 + x = -6.34428877 Solving -5.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.34428877 + 5.5 x = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 x = -0.84428877 Simplifying x = -0.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.84428877, -0.84428877}Solution
x = {11.84428877, -0.84428877}
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