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Simplifying 48x2 + -20x + -10620 = 0 Reorder the terms: -10620 + -20x + 48x2 = 0 Solving -10620 + -20x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2655 + -5x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2655 + -5x + 12x2)' equal to zero and attempt to solve: Simplifying -2655 + -5x + 12x2 = 0 Solving -2655 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -221.25 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '221.25' to each side of the equation. -221.25 + -0.4166666667x + 221.25 + x2 = 0 + 221.25 Reorder the terms: -221.25 + 221.25 + -0.4166666667x + x2 = 0 + 221.25 Combine like terms: -221.25 + 221.25 = 0.00 0.00 + -0.4166666667x + x2 = 0 + 221.25 -0.4166666667x + x2 = 0 + 221.25 Combine like terms: 0 + 221.25 = 221.25 -0.4166666667x + x2 = 221.25 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = 221.25 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 221.25 + 0.04340277781 Combine like terms: 221.25 + 0.04340277781 = 221.29340277781 0.04340277781 + -0.4166666667x + x2 = 221.29340277781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 221.29340277781 Calculate the square root of the right side: 14.875933678 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 14.875933678 and -14.875933678.Subproblem 1
x + -0.2083333334 = 14.875933678 Simplifying x + -0.2083333334 = 14.875933678 Reorder the terms: -0.2083333334 + x = 14.875933678 Solving -0.2083333334 + x = 14.875933678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = 14.875933678 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 14.875933678 + 0.2083333334 x = 14.875933678 + 0.2083333334 Combine like terms: 14.875933678 + 0.2083333334 = 15.0842670114 x = 15.0842670114 Simplifying x = 15.0842670114Subproblem 2
x + -0.2083333334 = -14.875933678 Simplifying x + -0.2083333334 = -14.875933678 Reorder the terms: -0.2083333334 + x = -14.875933678 Solving -0.2083333334 + x = -14.875933678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = -14.875933678 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -14.875933678 + 0.2083333334 x = -14.875933678 + 0.2083333334 Combine like terms: -14.875933678 + 0.2083333334 = -14.6676003446 x = -14.6676003446 Simplifying x = -14.6676003446Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.0842670114, -14.6676003446}Solution
x = {15.0842670114, -14.6676003446}
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