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Simplifying 6x2 + 66x + -180 = 0 Reorder the terms: -180 + 66x + 6x2 = 0 Solving -180 + 66x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-30 + 11x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-30 + 11x + x2)' equal to zero and attempt to solve: Simplifying -30 + 11x + x2 = 0 Solving -30 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 11x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 11x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11x + x2 = 0 + 30 11x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 11x + x2 = 30 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 = 30 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + 11x + x2 = 60.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 5.5 = 7.762087348 Simplifying x + 5.5 = 7.762087348 Reorder the terms: 5.5 + x = 7.762087348 Solving 5.5 + x = 7.762087348 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 = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.762087348 + -5.5 x = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 x = 2.262087348 Simplifying x = 2.262087348Subproblem 2
x + 5.5 = -7.762087348 Simplifying x + 5.5 = -7.762087348 Reorder the terms: 5.5 + x = -7.762087348 Solving 5.5 + x = -7.762087348 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 = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.762087348 + -5.5 x = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 x = -13.262087348 Simplifying x = -13.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.262087348, -13.262087348}Solution
x = {2.262087348, -13.262087348}
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