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Simplifying x2 + -1x = 512 Reorder the terms: -1x + x2 = 512 Solving -1x + x2 = 512 Solving for variable 'x'. Reorder the terms: -512 + -1x + x2 = 512 + -512 Combine like terms: 512 + -512 = 0 -512 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '512' to each side of the equation. -512 + -1x + 512 + x2 = 0 + 512 Reorder the terms: -512 + 512 + -1x + x2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + -1x + x2 = 0 + 512 -1x + x2 = 0 + 512 Combine like terms: 0 + 512 = 512 -1x + x2 = 512 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 = 512 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 512 + 0.25 Combine like terms: 512 + 0.25 = 512.25 0.25 + -1x + x2 = 512.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 512.25 Calculate the square root of the right side: 22.632940596 Break this problem into two subproblems by setting (x + -0.5) equal to 22.632940596 and -22.632940596.Subproblem 1
x + -0.5 = 22.632940596 Simplifying x + -0.5 = 22.632940596 Reorder the terms: -0.5 + x = 22.632940596 Solving -0.5 + x = 22.632940596 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 = 22.632940596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 22.632940596 + 0.5 x = 22.632940596 + 0.5 Combine like terms: 22.632940596 + 0.5 = 23.132940596 x = 23.132940596 Simplifying x = 23.132940596Subproblem 2
x + -0.5 = -22.632940596 Simplifying x + -0.5 = -22.632940596 Reorder the terms: -0.5 + x = -22.632940596 Solving -0.5 + x = -22.632940596 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 = -22.632940596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -22.632940596 + 0.5 x = -22.632940596 + 0.5 Combine like terms: -22.632940596 + 0.5 = -22.132940596 x = -22.132940596 Simplifying x = -22.132940596Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.132940596, -22.132940596}
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