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Simplifying 0 = 8 + -9x2 + 13x Reorder the terms: 0 = 8 + 13x + -9x2 Solving 0 = 8 + 13x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -13x + 9x2 = 8 + 13x + -9x2 + -8 + -13x + 9x2 Reorder the terms: -8 + -13x + 9x2 = 8 + -8 + 13x + -13x + -9x2 + 9x2 Combine like terms: 8 + -8 = 0 -8 + -13x + 9x2 = 0 + 13x + -13x + -9x2 + 9x2 -8 + -13x + 9x2 = 13x + -13x + -9x2 + 9x2 Combine like terms: 13x + -13x = 0 -8 + -13x + 9x2 = 0 + -9x2 + 9x2 -8 + -13x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -8 + -13x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -1.444444444x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -1.444444444x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -1.444444444x + x2 = 0 + 0.8888888889 -1.444444444x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -1.444444444x + x2 = 0.8888888889 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = 0.8888888889 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = 0.8888888889 + 0.5216049380 Combine like terms: 0.8888888889 + 0.5216049380 = 1.4104938269 0.5216049380 + -1.444444444x + x2 = 1.4104938269 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 1.4104938269 Calculate the square root of the right side: 1.187642129 Break this problem into two subproblems by setting (x + -0.722222222) equal to 1.187642129 and -1.187642129.Subproblem 1
x + -0.722222222 = 1.187642129 Simplifying x + -0.722222222 = 1.187642129 Reorder the terms: -0.722222222 + x = 1.187642129 Solving -0.722222222 + x = 1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 1.187642129 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 1.187642129 + 0.722222222 x = 1.187642129 + 0.722222222 Combine like terms: 1.187642129 + 0.722222222 = 1.909864351 x = 1.909864351 Simplifying x = 1.909864351Subproblem 2
x + -0.722222222 = -1.187642129 Simplifying x + -0.722222222 = -1.187642129 Reorder the terms: -0.722222222 + x = -1.187642129 Solving -0.722222222 + x = -1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -1.187642129 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -1.187642129 + 0.722222222 x = -1.187642129 + 0.722222222 Combine like terms: -1.187642129 + 0.722222222 = -0.465419907 x = -0.465419907 Simplifying x = -0.465419907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.909864351, -0.465419907}
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