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Simplifying x + 10 = 9x2 + -1 Reorder the terms: 10 + x = 9x2 + -1 Reorder the terms: 10 + x = -1 + 9x2 Solving 10 + x = -1 + 9x2 Solving for variable 'x'. Reorder the terms: 10 + 1 + x + -9x2 = -1 + 9x2 + 1 + -9x2 Combine like terms: 10 + 1 = 11 11 + x + -9x2 = -1 + 9x2 + 1 + -9x2 Reorder the terms: 11 + x + -9x2 = -1 + 1 + 9x2 + -9x2 Combine like terms: -1 + 1 = 0 11 + x + -9x2 = 0 + 9x2 + -9x2 11 + x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 11 + x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.222222222 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -0.1111111111x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -0.1111111111x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 1.222222222 -0.1111111111x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -0.1111111111x + x2 = 1.222222222 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111x + 0.25 + x2 = 1.222222222 + 0.25 Reorder the terms: 0.25 + -0.1111111111x + x2 = 1.222222222 + 0.25 Combine like terms: 1.222222222 + 0.25 = 1.472222222 0.25 + -0.1111111111x + x2 = 1.472222222 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.472222222 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (x + 0.5) equal to 1.213351648 and -1.213351648.Subproblem 1
x + 0.5 = 1.213351648 Simplifying x + 0.5 = 1.213351648 Reorder the terms: 0.5 + x = 1.213351648 Solving 0.5 + x = 1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.213351648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.213351648 + -0.5 x = 1.213351648 + -0.5 Combine like terms: 1.213351648 + -0.5 = 0.713351648 x = 0.713351648 Simplifying x = 0.713351648Subproblem 2
x + 0.5 = -1.213351648 Simplifying x + 0.5 = -1.213351648 Reorder the terms: 0.5 + x = -1.213351648 Solving 0.5 + x = -1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.213351648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.213351648 + -0.5 x = -1.213351648 + -0.5 Combine like terms: -1.213351648 + -0.5 = -1.713351648 x = -1.713351648 Simplifying x = -1.713351648Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.713351648, -1.713351648}
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