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Simplifying x2 = 57 + -1x Solving x2 = 57 + -1x Solving for variable 'x'. Reorder the terms: -57 + x + x2 = 57 + -1x + -57 + x Reorder the terms: -57 + x + x2 = 57 + -57 + -1x + x Combine like terms: 57 + -57 = 0 -57 + x + x2 = 0 + -1x + x -57 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -57 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + x + x2 = 0 + 57 x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 x + x2 = 57 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. x + 0.25 + x2 = 57 + 0.25 Reorder the terms: 0.25 + x + x2 = 57 + 0.25 Combine like terms: 57 + 0.25 = 57.25 0.25 + x + x2 = 57.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + 0.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + 0.5 = 7.566372975 Simplifying x + 0.5 = 7.566372975 Reorder the terms: 0.5 + x = 7.566372975 Solving 0.5 + x = 7.566372975 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 = 7.566372975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.566372975 + -0.5 x = 7.566372975 + -0.5 Combine like terms: 7.566372975 + -0.5 = 7.066372975 x = 7.066372975 Simplifying x = 7.066372975Subproblem 2
x + 0.5 = -7.566372975 Simplifying x + 0.5 = -7.566372975 Reorder the terms: 0.5 + x = -7.566372975 Solving 0.5 + x = -7.566372975 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 = -7.566372975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.566372975 + -0.5 x = -7.566372975 + -0.5 Combine like terms: -7.566372975 + -0.5 = -8.066372975 x = -8.066372975 Simplifying x = -8.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.066372975, -8.066372975}
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