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Simplifying 4x2 + -66x + 150 = 0 Reorder the terms: 150 + -66x + 4x2 = 0 Solving 150 + -66x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -33x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -33x + 2x2)' equal to zero and attempt to solve: Simplifying 75 + -33x + 2x2 = 0 Solving 75 + -33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 37.5 + -16.5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -16.5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -16.5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -16.5x + x2 = 0 + -37.5 -16.5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -16.5x + x2 = -37.5 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 = -37.5 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -37.5 + 68.0625 Combine like terms: -37.5 + 68.0625 = 30.5625 68.0625 + -16.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + -8.25) equal to 5.528336097 and -5.528336097.Subproblem 1
x + -8.25 = 5.528336097 Simplifying x + -8.25 = 5.528336097 Reorder the terms: -8.25 + x = 5.528336097 Solving -8.25 + x = 5.528336097 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 = 5.528336097 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 5.528336097 + 8.25 x = 5.528336097 + 8.25 Combine like terms: 5.528336097 + 8.25 = 13.778336097 x = 13.778336097 Simplifying x = 13.778336097Subproblem 2
x + -8.25 = -5.528336097 Simplifying x + -8.25 = -5.528336097 Reorder the terms: -8.25 + x = -5.528336097 Solving -8.25 + x = -5.528336097 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 = -5.528336097 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -5.528336097 + 8.25 x = -5.528336097 + 8.25 Combine like terms: -5.528336097 + 8.25 = 2.721663903 x = 2.721663903 Simplifying x = 2.721663903Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.778336097, 2.721663903}Solution
x = {13.778336097, 2.721663903}
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