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Simplifying x2 + 2x + -560 = 0 Reorder the terms: -560 + 2x + x2 = 0 Solving -560 + 2x + x2 = 0 Solving for variable 'x'. 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 = 22.685438565 x = 22.685438565 Simplifying x = 22.685438565Subproblem 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 = -24.685438565 x = -24.685438565 Simplifying x = -24.685438565Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.685438565, -24.685438565}
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