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Simplifying -24x2 + 60x + 38 = 0 Reorder the terms: 38 + 60x + -24x2 = 0 Solving 38 + 60x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 30x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 30x + -12x2)' equal to zero and attempt to solve: Simplifying 19 + 30x + -12x2 = 0 Solving 19 + 30x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.583333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + -2.5x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + -2.5x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 1.583333333 -2.5x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 -2.5x + x2 = 1.583333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.583333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.583333333 + 1.5625 Combine like terms: 1.583333333 + 1.5625 = 3.145833333 1.5625 + -2.5x + x2 = 3.145833333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 3.145833333 Calculate the square root of the right side: 1.773649721 Break this problem into two subproblems by setting (x + -1.25) equal to 1.773649721 and -1.773649721.Subproblem 1
x + -1.25 = 1.773649721 Simplifying x + -1.25 = 1.773649721 Reorder the terms: -1.25 + x = 1.773649721 Solving -1.25 + x = 1.773649721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.773649721 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.773649721 + 1.25 x = 1.773649721 + 1.25 Combine like terms: 1.773649721 + 1.25 = 3.023649721 x = 3.023649721 Simplifying x = 3.023649721Subproblem 2
x + -1.25 = -1.773649721 Simplifying x + -1.25 = -1.773649721 Reorder the terms: -1.25 + x = -1.773649721 Solving -1.25 + x = -1.773649721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.773649721 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.773649721 + 1.25 x = -1.773649721 + 1.25 Combine like terms: -1.773649721 + 1.25 = -0.523649721 x = -0.523649721 Simplifying x = -0.523649721Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.023649721, -0.523649721}Solution
x = {3.023649721, -0.523649721}
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