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Simplifying x2 + 16 = 100 + -1x Reorder the terms: 16 + x2 = 100 + -1x Solving 16 + x2 = 100 + -1x Solving for variable 'x'. Reorder the terms: 16 + -100 + x + x2 = 100 + -1x + -100 + x Combine like terms: 16 + -100 = -84 -84 + x + x2 = 100 + -1x + -100 + x Reorder the terms: -84 + x + x2 = 100 + -100 + -1x + x Combine like terms: 100 + -100 = 0 -84 + x + x2 = 0 + -1x + x -84 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -84 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + x + x2 = 0 + 84 x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 x + x2 = 84 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 = 84 + 0.25 Reorder the terms: 0.25 + x + x2 = 84 + 0.25 Combine like terms: 84 + 0.25 = 84.25 0.25 + x + x2 = 84.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 0.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 0.5 = 9.178779875 Simplifying x + 0.5 = 9.178779875 Reorder the terms: 0.5 + x = 9.178779875 Solving 0.5 + x = 9.178779875 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 = 9.178779875 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.178779875 + -0.5 x = 9.178779875 + -0.5 Combine like terms: 9.178779875 + -0.5 = 8.678779875 x = 8.678779875 Simplifying x = 8.678779875Subproblem 2
x + 0.5 = -9.178779875 Simplifying x + 0.5 = -9.178779875 Reorder the terms: 0.5 + x = -9.178779875 Solving 0.5 + x = -9.178779875 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 = -9.178779875 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.178779875 + -0.5 x = -9.178779875 + -0.5 Combine like terms: -9.178779875 + -0.5 = -9.678779875 x = -9.678779875 Simplifying x = -9.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.678779875, -9.678779875}
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