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Simplifying x2 = 23.5 + -1x Solving x2 = 23.5 + -1x Solving for variable 'x'. Reorder the terms: -23.5 + x + x2 = 23.5 + -1x + -23.5 + x Reorder the terms: -23.5 + x + x2 = 23.5 + -23.5 + -1x + x Combine like terms: 23.5 + -23.5 = 0.0 -23.5 + x + x2 = 0.0 + -1x + x -23.5 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -23.5 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x + x2 = 0 + 23.5 x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 x + x2 = 23.5 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 = 23.5 + 0.25 Reorder the terms: 0.25 + x + x2 = 23.5 + 0.25 Combine like terms: 23.5 + 0.25 = 23.75 0.25 + x + x2 = 23.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (x + 0.5) equal to 4.873397172 and -4.873397172.Subproblem 1
x + 0.5 = 4.873397172 Simplifying x + 0.5 = 4.873397172 Reorder the terms: 0.5 + x = 4.873397172 Solving 0.5 + x = 4.873397172 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 = 4.873397172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.873397172 + -0.5 x = 4.873397172 + -0.5 Combine like terms: 4.873397172 + -0.5 = 4.373397172 x = 4.373397172 Simplifying x = 4.373397172Subproblem 2
x + 0.5 = -4.873397172 Simplifying x + 0.5 = -4.873397172 Reorder the terms: 0.5 + x = -4.873397172 Solving 0.5 + x = -4.873397172 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 = -4.873397172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.873397172 + -0.5 x = -4.873397172 + -0.5 Combine like terms: -4.873397172 + -0.5 = -5.373397172 x = -5.373397172 Simplifying x = -5.373397172Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.373397172, -5.373397172}
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