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Simplifying 6x2 + -13x + -69 = 0 Reorder the terms: -69 + -13x + 6x2 = 0 Solving -69 + -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'. -11.5 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -2.166666667x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -2.166666667x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -2.166666667x + x2 = 0 + 11.5 -2.166666667x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -2.166666667x + x2 = 11.5 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 = 11.5 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 11.5 + 1.173611113 Combine like terms: 11.5 + 1.173611113 = 12.673611113 1.173611113 + -2.166666667x + x2 = 12.673611113 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 12.673611113 Calculate the square root of the right side: 3.560001561 Break this problem into two subproblems by setting (x + -1.083333334) equal to 3.560001561 and -3.560001561.Subproblem 1
x + -1.083333334 = 3.560001561 Simplifying x + -1.083333334 = 3.560001561 Reorder the terms: -1.083333334 + x = 3.560001561 Solving -1.083333334 + x = 3.560001561 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 = 3.560001561 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 3.560001561 + 1.083333334 x = 3.560001561 + 1.083333334 Combine like terms: 3.560001561 + 1.083333334 = 4.643334895 x = 4.643334895 Simplifying x = 4.643334895Subproblem 2
x + -1.083333334 = -3.560001561 Simplifying x + -1.083333334 = -3.560001561 Reorder the terms: -1.083333334 + x = -3.560001561 Solving -1.083333334 + x = -3.560001561 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 = -3.560001561 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -3.560001561 + 1.083333334 x = -3.560001561 + 1.083333334 Combine like terms: -3.560001561 + 1.083333334 = -2.476668227 x = -2.476668227 Simplifying x = -2.476668227Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.643334895, -2.476668227}
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