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Simplifying x(x + -2) = 560 Reorder the terms: x(-2 + x) = 560 (-2 * x + x * x) = 560 (-2x + x2) = 560 Solving -2x + x2 = 560 Solving for variable 'x'. Reorder the terms: -560 + -2x + x2 = 560 + -560 Combine like terms: 560 + -560 = 0 -560 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '560' to each side of the equation. -560 + -2x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + -2x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + -2x + x2 = 0 + 560 -2x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 -2x + x2 = 560 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 560 + 1 Reorder the terms: 1 + -2x + x2 = 560 + 1 Combine like terms: 560 + 1 = 561 1 + -2x + x2 = 561 Factor a perfect square on the left side: (x + -1)(x + -1) = 561 Calculate the square root of the right side: 23.685438565 Break this problem into two subproblems by setting (x + -1) equal to 23.685438565 and -23.685438565.Subproblem 1
x + -1 = 23.685438565 Simplifying x + -1 = 23.685438565 Reorder the terms: -1 + x = 23.685438565 Solving -1 + x = 23.685438565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 23.685438565 + 1 Combine like terms: -1 + 1 = 0 0 + x = 23.685438565 + 1 x = 23.685438565 + 1 Combine like terms: 23.685438565 + 1 = 24.685438565 x = 24.685438565 Simplifying x = 24.685438565Subproblem 2
x + -1 = -23.685438565 Simplifying x + -1 = -23.685438565 Reorder the terms: -1 + x = -23.685438565 Solving -1 + x = -23.685438565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -23.685438565 + 1 Combine like terms: -1 + 1 = 0 0 + x = -23.685438565 + 1 x = -23.685438565 + 1 Combine like terms: -23.685438565 + 1 = -22.685438565 x = -22.685438565 Simplifying x = -22.685438565Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.685438565, -22.685438565}
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