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Simplifying 3x2 + -26x + -15 = 0 Reorder the terms: -15 + -26x + 3x2 = 0 Solving -15 + -26x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -8.666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.666666667x + x2 = 0 + 5 -8.666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.666666667x + x2 = 5 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 = 5 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = 5 + 18.77777778 Combine like terms: 5 + 18.77777778 = 23.77777778 18.77777778 + -8.666666667x + x2 = 23.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 23.77777778 Calculate the square root of the right side: 4.87624628 Break this problem into two subproblems by setting (x + -4.333333334) equal to 4.87624628 and -4.87624628.Subproblem 1
x + -4.333333334 = 4.87624628 Simplifying x + -4.333333334 = 4.87624628 Reorder the terms: -4.333333334 + x = 4.87624628 Solving -4.333333334 + x = 4.87624628 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 = 4.87624628 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 4.87624628 + 4.333333334 x = 4.87624628 + 4.333333334 Combine like terms: 4.87624628 + 4.333333334 = 9.209579614 x = 9.209579614 Simplifying x = 9.209579614Subproblem 2
x + -4.333333334 = -4.87624628 Simplifying x + -4.333333334 = -4.87624628 Reorder the terms: -4.333333334 + x = -4.87624628 Solving -4.333333334 + x = -4.87624628 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 = -4.87624628 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -4.87624628 + 4.333333334 x = -4.87624628 + 4.333333334 Combine like terms: -4.87624628 + 4.333333334 = -0.542912946 x = -0.542912946 Simplifying x = -0.542912946Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.209579614, -0.542912946}
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