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Simplifying x2 + x = 456 Reorder the terms: x + x2 = 456 Solving x + x2 = 456 Solving for variable 'x'. Reorder the terms: -456 + x + x2 = 456 + -456 Combine like terms: 456 + -456 = 0 -456 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '456' to each side of the equation. -456 + x + 456 + x2 = 0 + 456 Reorder the terms: -456 + 456 + x + x2 = 0 + 456 Combine like terms: -456 + 456 = 0 0 + x + x2 = 0 + 456 x + x2 = 0 + 456 Combine like terms: 0 + 456 = 456 x + x2 = 456 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 = 456 + 0.25 Reorder the terms: 0.25 + x + x2 = 456 + 0.25 Combine like terms: 456 + 0.25 = 456.25 0.25 + x + x2 = 456.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 456.25 Calculate the square root of the right side: 21.360009363 Break this problem into two subproblems by setting (x + 0.5) equal to 21.360009363 and -21.360009363.Subproblem 1
x + 0.5 = 21.360009363 Simplifying x + 0.5 = 21.360009363 Reorder the terms: 0.5 + x = 21.360009363 Solving 0.5 + x = 21.360009363 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 = 21.360009363 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 21.360009363 + -0.5 x = 21.360009363 + -0.5 Combine like terms: 21.360009363 + -0.5 = 20.860009363 x = 20.860009363 Simplifying x = 20.860009363Subproblem 2
x + 0.5 = -21.360009363 Simplifying x + 0.5 = -21.360009363 Reorder the terms: 0.5 + x = -21.360009363 Solving 0.5 + x = -21.360009363 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 = -21.360009363 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -21.360009363 + -0.5 x = -21.360009363 + -0.5 Combine like terms: -21.360009363 + -0.5 = -21.860009363 x = -21.860009363 Simplifying x = -21.860009363Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.860009363, -21.860009363}
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