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Simplifying 6x2 + -13x + -9 = 0 Reorder the terms: -9 + -13x + 6x2 = 0 Solving -9 + -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'. -1.5 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.166666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.166666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.166666667x + x2 = 0 + 1.5 -2.166666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.166666667x + x2 = 1.5 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 = 1.5 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 1.5 + 1.173611113 Combine like terms: 1.5 + 1.173611113 = 2.673611113 1.173611113 + -2.166666667x + x2 = 2.673611113 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 2.673611113 Calculate the square root of the right side: 1.635118073 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.635118073 and -1.635118073.Subproblem 1
x + -1.083333334 = 1.635118073 Simplifying x + -1.083333334 = 1.635118073 Reorder the terms: -1.083333334 + x = 1.635118073 Solving -1.083333334 + x = 1.635118073 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 = 1.635118073 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.635118073 + 1.083333334 x = 1.635118073 + 1.083333334 Combine like terms: 1.635118073 + 1.083333334 = 2.718451407 x = 2.718451407 Simplifying x = 2.718451407Subproblem 2
x + -1.083333334 = -1.635118073 Simplifying x + -1.083333334 = -1.635118073 Reorder the terms: -1.083333334 + x = -1.635118073 Solving -1.083333334 + x = -1.635118073 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 = -1.635118073 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.635118073 + 1.083333334 x = -1.635118073 + 1.083333334 Combine like terms: -1.635118073 + 1.083333334 = -0.551784739 x = -0.551784739 Simplifying x = -0.551784739Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.718451407, -0.551784739}
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