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Simplifying 4x2 + 66x + -240 = 0 Reorder the terms: -240 + 66x + 4x2 = 0 Solving -240 + 66x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + 33x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + 33x + 2x2)' equal to zero and attempt to solve: Simplifying -120 + 33x + 2x2 = 0 Solving -120 + 33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + 16.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 16.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 16.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 16.5x + x2 = 0 + 60 16.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 16.5x + x2 = 60 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = 60 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 60 + 68.0625 Combine like terms: 60 + 68.0625 = 128.0625 68.0625 + 16.5x + x2 = 128.0625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 128.0625 Calculate the square root of the right side: 11.316470298 Break this problem into two subproblems by setting (x + 8.25) equal to 11.316470298 and -11.316470298.Subproblem 1
x + 8.25 = 11.316470298 Simplifying x + 8.25 = 11.316470298 Reorder the terms: 8.25 + x = 11.316470298 Solving 8.25 + x = 11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 11.316470298 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 11.316470298 + -8.25 x = 11.316470298 + -8.25 Combine like terms: 11.316470298 + -8.25 = 3.066470298 x = 3.066470298 Simplifying x = 3.066470298Subproblem 2
x + 8.25 = -11.316470298 Simplifying x + 8.25 = -11.316470298 Reorder the terms: 8.25 + x = -11.316470298 Solving 8.25 + x = -11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -11.316470298 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -11.316470298 + -8.25 x = -11.316470298 + -8.25 Combine like terms: -11.316470298 + -8.25 = -19.566470298 x = -19.566470298 Simplifying x = -19.566470298Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.066470298, -19.566470298}Solution
x = {3.066470298, -19.566470298}
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