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Simplifying x * x + 1x + -1 = 210 Multiply x * x x2 + 1x + -1 = 210 Reorder the terms: -1 + 1x + x2 = 210 Solving -1 + 1x + x2 = 210 Solving for variable 'x'. Reorder the terms: -1 + -210 + 1x + x2 = 210 + -210 Combine like terms: -1 + -210 = -211 -211 + 1x + x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -211 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '211' to each side of the equation. -211 + 1x + 211 + x2 = 0 + 211 Reorder the terms: -211 + 211 + 1x + x2 = 0 + 211 Combine like terms: -211 + 211 = 0 0 + 1x + x2 = 0 + 211 1x + x2 = 0 + 211 Combine like terms: 0 + 211 = 211 1x + x2 = 211 The x term is 1x. 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 = 211 + 0.25 Reorder the terms: 0.25 + x + x2 = 211 + 0.25 Combine like terms: 211 + 0.25 = 211.25 0.25 + x + x2 = 211.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 211.25 Calculate the square root of the right side: 14.534441854 Break this problem into two subproblems by setting (x + 0.5) equal to 14.534441854 and -14.534441854.Subproblem 1
x + 0.5 = 14.534441854 Simplifying x + 0.5 = 14.534441854 Reorder the terms: 0.5 + x = 14.534441854 Solving 0.5 + x = 14.534441854 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 = 14.534441854 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.534441854 + -0.5 x = 14.534441854 + -0.5 Combine like terms: 14.534441854 + -0.5 = 14.034441854 x = 14.034441854 Simplifying x = 14.034441854Subproblem 2
x + 0.5 = -14.534441854 Simplifying x + 0.5 = -14.534441854 Reorder the terms: 0.5 + x = -14.534441854 Solving 0.5 + x = -14.534441854 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 = -14.534441854 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.534441854 + -0.5 x = -14.534441854 + -0.5 Combine like terms: -14.534441854 + -0.5 = -15.034441854 x = -15.034441854 Simplifying x = -15.034441854Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.034441854, -15.034441854}
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