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Simplifying 6x2 + -13x + -91 = 0 Reorder the terms: -91 + -13x + 6x2 = 0 Solving -91 + -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'. -15.16666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '15.16666667' to each side of the equation. -15.16666667 + -2.166666667x + 15.16666667 + x2 = 0 + 15.16666667 Reorder the terms: -15.16666667 + 15.16666667 + -2.166666667x + x2 = 0 + 15.16666667 Combine like terms: -15.16666667 + 15.16666667 = 0.00000000 0.00000000 + -2.166666667x + x2 = 0 + 15.16666667 -2.166666667x + x2 = 0 + 15.16666667 Combine like terms: 0 + 15.16666667 = 15.16666667 -2.166666667x + x2 = 15.16666667 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 = 15.16666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 15.16666667 + 1.173611113 Combine like terms: 15.16666667 + 1.173611113 = 16.340277783 1.173611113 + -2.166666667x + x2 = 16.340277783 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 16.340277783 Calculate the square root of the right side: 4.042310946 Break this problem into two subproblems by setting (x + -1.083333334) equal to 4.042310946 and -4.042310946.Subproblem 1
x + -1.083333334 = 4.042310946 Simplifying x + -1.083333334 = 4.042310946 Reorder the terms: -1.083333334 + x = 4.042310946 Solving -1.083333334 + x = 4.042310946 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 = 4.042310946 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 4.042310946 + 1.083333334 x = 4.042310946 + 1.083333334 Combine like terms: 4.042310946 + 1.083333334 = 5.12564428 x = 5.12564428 Simplifying x = 5.12564428Subproblem 2
x + -1.083333334 = -4.042310946 Simplifying x + -1.083333334 = -4.042310946 Reorder the terms: -1.083333334 + x = -4.042310946 Solving -1.083333334 + x = -4.042310946 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 = -4.042310946 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -4.042310946 + 1.083333334 x = -4.042310946 + 1.083333334 Combine like terms: -4.042310946 + 1.083333334 = -2.958977612 x = -2.958977612 Simplifying x = -2.958977612Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.12564428, -2.958977612}
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