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Simplifying (x) = 110 + 0.5 + -1x2 x = 110 + 0.5 + -1x2 Combine like terms: 110 + 0.5 = 110.5 x = 110.5 + -1x2 Solving x = 110.5 + -1x2 Solving for variable 'x'. Reorder the terms: -110.5 + x + x2 = 110.5 + -1x2 + -110.5 + x2 Reorder the terms: -110.5 + x + x2 = 110.5 + -110.5 + -1x2 + x2 Combine like terms: 110.5 + -110.5 = 0.0 -110.5 + x + x2 = 0.0 + -1x2 + x2 -110.5 + x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -110.5 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110.5' to each side of the equation. -110.5 + x + 110.5 + x2 = 0 + 110.5 Reorder the terms: -110.5 + 110.5 + x + x2 = 0 + 110.5 Combine like terms: -110.5 + 110.5 = 0.0 0.0 + x + x2 = 0 + 110.5 x + x2 = 0 + 110.5 Combine like terms: 0 + 110.5 = 110.5 x + x2 = 110.5 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 = 110.5 + 0.25 Reorder the terms: 0.25 + x + x2 = 110.5 + 0.25 Combine like terms: 110.5 + 0.25 = 110.75 0.25 + x + x2 = 110.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 110.75 Calculate the square root of the right side: 10.52378259 Break this problem into two subproblems by setting (x + 0.5) equal to 10.52378259 and -10.52378259.Subproblem 1
x + 0.5 = 10.52378259 Simplifying x + 0.5 = 10.52378259 Reorder the terms: 0.5 + x = 10.52378259 Solving 0.5 + x = 10.52378259 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 = 10.52378259 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.52378259 + -0.5 x = 10.52378259 + -0.5 Combine like terms: 10.52378259 + -0.5 = 10.02378259 x = 10.02378259 Simplifying x = 10.02378259Subproblem 2
x + 0.5 = -10.52378259 Simplifying x + 0.5 = -10.52378259 Reorder the terms: 0.5 + x = -10.52378259 Solving 0.5 + x = -10.52378259 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 = -10.52378259 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.52378259 + -0.5 x = -10.52378259 + -0.5 Combine like terms: -10.52378259 + -0.5 = -11.02378259 x = -11.02378259 Simplifying x = -11.02378259Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.02378259, -11.02378259}
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