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Simplifying x2 = x + 99 Reorder the terms: x2 = 99 + x Solving x2 = 99 + x Solving for variable 'x'. Reorder the terms: -99 + -1x + x2 = 99 + x + -99 + -1x Reorder the terms: -99 + -1x + x2 = 99 + -99 + x + -1x Combine like terms: 99 + -99 = 0 -99 + -1x + x2 = 0 + x + -1x -99 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -99 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -1x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -1x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -1x + x2 = 0 + 99 -1x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -1x + x2 = 99 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. -1x + 0.25 + x2 = 99 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 99 + 0.25 Combine like terms: 99 + 0.25 = 99.25 0.25 + -1x + x2 = 99.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (x + -0.5) equal to 9.962429423 and -9.962429423.Subproblem 1
x + -0.5 = 9.962429423 Simplifying x + -0.5 = 9.962429423 Reorder the terms: -0.5 + x = 9.962429423 Solving -0.5 + x = 9.962429423 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 = 9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.962429423 + 0.5 x = 9.962429423 + 0.5 Combine like terms: 9.962429423 + 0.5 = 10.462429423 x = 10.462429423 Simplifying x = 10.462429423Subproblem 2
x + -0.5 = -9.962429423 Simplifying x + -0.5 = -9.962429423 Reorder the terms: -0.5 + x = -9.962429423 Solving -0.5 + x = -9.962429423 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 = -9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.962429423 + 0.5 x = -9.962429423 + 0.5 Combine like terms: -9.962429423 + 0.5 = -9.462429423 x = -9.462429423 Simplifying x = -9.462429423Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.462429423, -9.462429423}
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