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Simplifying 6x2 + 66x + -540 = 0 Reorder the terms: -540 + 66x + 6x2 = 0 Solving -540 + 66x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-90 + 11x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-90 + 11x + x2)' equal to zero and attempt to solve: Simplifying -90 + 11x + x2 = 0 Solving -90 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 11x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 11x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 11x + x2 = 0 + 90 11x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 11x + x2 = 90 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 = 90 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 90 + 30.25 Combine like terms: 90 + 30.25 = 120.25 30.25 + 11x + x2 = 120.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 5.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 5.5 = 10.9658561 Simplifying x + 5.5 = 10.9658561 Reorder the terms: 5.5 + x = 10.9658561 Solving 5.5 + x = 10.9658561 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 = 10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 10.9658561 + -5.5 x = 10.9658561 + -5.5 Combine like terms: 10.9658561 + -5.5 = 5.4658561 x = 5.4658561 Simplifying x = 5.4658561Subproblem 2
x + 5.5 = -10.9658561 Simplifying x + 5.5 = -10.9658561 Reorder the terms: 5.5 + x = -10.9658561 Solving 5.5 + x = -10.9658561 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 = -10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -10.9658561 + -5.5 x = -10.9658561 + -5.5 Combine like terms: -10.9658561 + -5.5 = -16.4658561 x = -16.4658561 Simplifying x = -16.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4658561, -16.4658561}Solution
x = {5.4658561, -16.4658561}
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