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Simplifying x2 + x + -92 = 0 Reorder the terms: -92 + x + x2 = 0 Solving -92 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + x + x2 = 0 + 92 x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 x + x2 = 92 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 = 92 + 0.25 Reorder the terms: 0.25 + x + x2 = 92 + 0.25 Combine like terms: 92 + 0.25 = 92.25 0.25 + x + x2 = 92.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 0.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 0.5 = 9.604686356 Simplifying x + 0.5 = 9.604686356 Reorder the terms: 0.5 + x = 9.604686356 Solving 0.5 + x = 9.604686356 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 = 9.604686356 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.604686356 + -0.5 x = 9.604686356 + -0.5 Combine like terms: 9.604686356 + -0.5 = 9.104686356 x = 9.104686356 Simplifying x = 9.104686356Subproblem 2
x + 0.5 = -9.604686356 Simplifying x + 0.5 = -9.604686356 Reorder the terms: 0.5 + x = -9.604686356 Solving 0.5 + x = -9.604686356 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 = -9.604686356 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.604686356 + -0.5 x = -9.604686356 + -0.5 Combine like terms: -9.604686356 + -0.5 = -10.104686356 x = -10.104686356 Simplifying x = -10.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.104686356, -10.104686356}
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