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Simplifying x2 + -1x = 560 Reorder the terms: -1x + x2 = 560 Solving -1x + x2 = 560 Solving for variable 'x'. Reorder the terms: -560 + -1x + x2 = 560 + -560 Combine like terms: 560 + -560 = 0 -560 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '560' to each side of the equation. -560 + -1x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + -1x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + -1x + x2 = 0 + 560 -1x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 -1x + x2 = 560 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 = 560 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 560 + 0.25 Combine like terms: 560 + 0.25 = 560.25 0.25 + -1x + x2 = 560.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 560.25 Calculate the square root of the right side: 23.669600757 Break this problem into two subproblems by setting (x + -0.5) equal to 23.669600757 and -23.669600757.Subproblem 1
x + -0.5 = 23.669600757 Simplifying x + -0.5 = 23.669600757 Reorder the terms: -0.5 + x = 23.669600757 Solving -0.5 + x = 23.669600757 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 = 23.669600757 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 23.669600757 + 0.5 x = 23.669600757 + 0.5 Combine like terms: 23.669600757 + 0.5 = 24.169600757 x = 24.169600757 Simplifying x = 24.169600757Subproblem 2
x + -0.5 = -23.669600757 Simplifying x + -0.5 = -23.669600757 Reorder the terms: -0.5 + x = -23.669600757 Solving -0.5 + x = -23.669600757 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 = -23.669600757 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -23.669600757 + 0.5 x = -23.669600757 + 0.5 Combine like terms: -23.669600757 + 0.5 = -23.169600757 x = -23.169600757 Simplifying x = -23.169600757Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.169600757, -23.169600757}
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