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Simplifying 2.17 = x2 + -1x Reorder the terms: 2.17 = -1x + x2 Solving 2.17 = -1x + x2 Solving for variable 'x'. Reorder the terms: 2.17 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 2.17 + x + -1x2 = 0 + x2 + -1x2 2.17 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2.17 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2.17 + -1x + x2 = 0 Move the constant term to the right: Add '2.17' to each side of the equation. -2.17 + -1x + 2.17 + x2 = 0 + 2.17 Reorder the terms: -2.17 + 2.17 + -1x + x2 = 0 + 2.17 Combine like terms: -2.17 + 2.17 = 0.00 0.00 + -1x + x2 = 0 + 2.17 -1x + x2 = 0 + 2.17 Combine like terms: 0 + 2.17 = 2.17 -1x + x2 = 2.17 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. -1x + 0.25 + x2 = 2.17 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.17 + 0.25 Combine like terms: 2.17 + 0.25 = 2.42 0.25 + -1x + x2 = 2.42 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.42 Calculate the square root of the right side: 1.555634919 Break this problem into two subproblems by setting (x + 0.5) equal to 1.555634919 and -1.555634919.Subproblem 1
x + 0.5 = 1.555634919 Simplifying x + 0.5 = 1.555634919 Reorder the terms: 0.5 + x = 1.555634919 Solving 0.5 + x = 1.555634919 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 = 1.555634919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.555634919 + -0.5 x = 1.555634919 + -0.5 Combine like terms: 1.555634919 + -0.5 = 1.055634919 x = 1.055634919 Simplifying x = 1.055634919Subproblem 2
x + 0.5 = -1.555634919 Simplifying x + 0.5 = -1.555634919 Reorder the terms: 0.5 + x = -1.555634919 Solving 0.5 + x = -1.555634919 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 = -1.555634919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.555634919 + -0.5 x = -1.555634919 + -0.5 Combine like terms: -1.555634919 + -0.5 = -2.055634919 x = -2.055634919 Simplifying x = -2.055634919Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.055634919, -2.055634919}
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