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Simplifying -6x2 + -13x + 102 = 0 Reorder the terms: 102 + -13x + -6x2 = 0 Solving 102 + -13x + -6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -17 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 2.166666667x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 2.166666667x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2.166666667x + x2 = 0 + 17 2.166666667x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 2.166666667x + x2 = 17 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 17 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 17 + 1.173611113 Combine like terms: 17 + 1.173611113 = 18.173611113 1.173611113 + 2.166666667x + x2 = 18.173611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 18.173611113 Calculate the square root of the right side: 4.263051854 Break this problem into two subproblems by setting (x + 1.083333334) equal to 4.263051854 and -4.263051854.Subproblem 1
x + 1.083333334 = 4.263051854 Simplifying x + 1.083333334 = 4.263051854 Reorder the terms: 1.083333334 + x = 4.263051854 Solving 1.083333334 + x = 4.263051854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 4.263051854 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 4.263051854 + -1.083333334 x = 4.263051854 + -1.083333334 Combine like terms: 4.263051854 + -1.083333334 = 3.17971852 x = 3.17971852 Simplifying x = 3.17971852Subproblem 2
x + 1.083333334 = -4.263051854 Simplifying x + 1.083333334 = -4.263051854 Reorder the terms: 1.083333334 + x = -4.263051854 Solving 1.083333334 + x = -4.263051854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -4.263051854 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -4.263051854 + -1.083333334 x = -4.263051854 + -1.083333334 Combine like terms: -4.263051854 + -1.083333334 = -5.346385188 x = -5.346385188 Simplifying x = -5.346385188Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17971852, -5.346385188}
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