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Simplifying 9x2 + -15x + -47 = 0 Reorder the terms: -47 + -15x + 9x2 = 0 Solving -47 + -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'. -5.222222222 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + -1.666666667x + 5.222222222 + x2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + -1.666666667x + x2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 5.222222222 -1.666666667x + x2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 -1.666666667x + x2 = 5.222222222 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 = 5.222222222 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 5.222222222 + 0.6944444447 Combine like terms: 5.222222222 + 0.6944444447 = 5.9166666667 0.6944444447 + -1.666666667x + x2 = 5.9166666667 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 5.9166666667 Calculate the square root of the right side: 2.43241992 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.43241992 and -2.43241992.Subproblem 1
x + -0.8333333335 = 2.43241992 Simplifying x + -0.8333333335 = 2.43241992 Reorder the terms: -0.8333333335 + x = 2.43241992 Solving -0.8333333335 + x = 2.43241992 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 = 2.43241992 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.43241992 + 0.8333333335 x = 2.43241992 + 0.8333333335 Combine like terms: 2.43241992 + 0.8333333335 = 3.2657532535 x = 3.2657532535 Simplifying x = 3.2657532535Subproblem 2
x + -0.8333333335 = -2.43241992 Simplifying x + -0.8333333335 = -2.43241992 Reorder the terms: -0.8333333335 + x = -2.43241992 Solving -0.8333333335 + x = -2.43241992 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 = -2.43241992 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.43241992 + 0.8333333335 x = -2.43241992 + 0.8333333335 Combine like terms: -2.43241992 + 0.8333333335 = -1.5990865865 x = -1.5990865865 Simplifying x = -1.5990865865Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2657532535, -1.5990865865}
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