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Simplifying 9x2 + 15x + -8 = 0 Reorder the terms: -8 + 15x + 9x2 = 0 Solving -8 + 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'. -0.8888888889 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 1.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 1.666666667x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.8888888889 1.666666667x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 1.666666667x + x2 = 0.8888888889 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 = 0.8888888889 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.8888888889 + 0.6944444447 Combine like terms: 0.8888888889 + 0.6944444447 = 1.5833333336 0.6944444447 + 1.666666667x + x2 = 1.5833333336 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.5833333336 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.258305739 and -1.258305739.Subproblem 1
x + 0.8333333335 = 1.258305739 Simplifying x + 0.8333333335 = 1.258305739 Reorder the terms: 0.8333333335 + x = 1.258305739 Solving 0.8333333335 + x = 1.258305739 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 = 1.258305739 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.258305739 + -0.8333333335 x = 1.258305739 + -0.8333333335 Combine like terms: 1.258305739 + -0.8333333335 = 0.4249724055 x = 0.4249724055 Simplifying x = 0.4249724055Subproblem 2
x + 0.8333333335 = -1.258305739 Simplifying x + 0.8333333335 = -1.258305739 Reorder the terms: 0.8333333335 + x = -1.258305739 Solving 0.8333333335 + x = -1.258305739 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 = -1.258305739 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.258305739 + -0.8333333335 x = -1.258305739 + -0.8333333335 Combine like terms: -1.258305739 + -0.8333333335 = -2.0916390725 x = -2.0916390725 Simplifying x = -2.0916390725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4249724055, -2.0916390725}
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