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Simplifying 9x2 + 15x + -56 = 0 Reorder the terms: -56 + 15x + 9x2 = 0 Solving -56 + 15x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.222222222 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + 1.666666667x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + 1.666666667x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 6.222222222 1.666666667x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 1.666666667x + x2 = 6.222222222 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 6.222222222 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 6.222222222 + 0.6944444447 Combine like terms: 6.222222222 + 0.6944444447 = 6.9166666667 0.6944444447 + 1.666666667x + x2 = 6.9166666667 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 6.9166666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.62995564 and -2.62995564.Subproblem 1
x + 0.8333333335 = 2.62995564 Simplifying x + 0.8333333335 = 2.62995564 Reorder the terms: 0.8333333335 + x = 2.62995564 Solving 0.8333333335 + x = 2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.62995564 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.62995564 + -0.8333333335 x = 2.62995564 + -0.8333333335 Combine like terms: 2.62995564 + -0.8333333335 = 1.7966223065 x = 1.7966223065 Simplifying x = 1.7966223065Subproblem 2
x + 0.8333333335 = -2.62995564 Simplifying x + 0.8333333335 = -2.62995564 Reorder the terms: 0.8333333335 + x = -2.62995564 Solving 0.8333333335 + x = -2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.62995564 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.62995564 + -0.8333333335 x = -2.62995564 + -0.8333333335 Combine like terms: -2.62995564 + -0.8333333335 = -3.4632889735 x = -3.4632889735 Simplifying x = -3.4632889735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7966223065, -3.4632889735}
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