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Simplifying 3x2 + -26x + -9 = 9 Reorder the terms: -9 + -26x + 3x2 = 9 Solving -9 + -26x + 3x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -9 + -26x + 3x2 = 9 + -9 Combine like terms: -9 + -9 = -18 -18 + -26x + 3x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -18 + -26x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -8.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -8.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8.666666667x + x2 = 0 + 6 -8.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8.666666667x + x2 = 6 The x term is -8.666666667x. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667x + 18.77777778 + x2 = 6 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = 6 + 18.77777778 Combine like terms: 6 + 18.77777778 = 24.77777778 18.77777778 + -8.666666667x + x2 = 24.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 24.77777778 Calculate the square root of the right side: 4.977728175 Break this problem into two subproblems by setting (x + -4.333333334) equal to 4.977728175 and -4.977728175.Subproblem 1
x + -4.333333334 = 4.977728175 Simplifying x + -4.333333334 = 4.977728175 Reorder the terms: -4.333333334 + x = 4.977728175 Solving -4.333333334 + x = 4.977728175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 4.977728175 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 4.977728175 + 4.333333334 x = 4.977728175 + 4.333333334 Combine like terms: 4.977728175 + 4.333333334 = 9.311061509 x = 9.311061509 Simplifying x = 9.311061509Subproblem 2
x + -4.333333334 = -4.977728175 Simplifying x + -4.333333334 = -4.977728175 Reorder the terms: -4.333333334 + x = -4.977728175 Solving -4.333333334 + x = -4.977728175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -4.977728175 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -4.977728175 + 4.333333334 x = -4.977728175 + 4.333333334 Combine like terms: -4.977728175 + 4.333333334 = -0.644394841 x = -0.644394841 Simplifying x = -0.644394841Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.311061509, -0.644394841}
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