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Simplifying x2 + 2x + -530 = 0 Reorder the terms: -530 + 2x + x2 = 0 Solving -530 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '530' to each side of the equation. -530 + 2x + 530 + x2 = 0 + 530 Reorder the terms: -530 + 530 + 2x + x2 = 0 + 530 Combine like terms: -530 + 530 = 0 0 + 2x + x2 = 0 + 530 2x + x2 = 0 + 530 Combine like terms: 0 + 530 = 530 2x + x2 = 530 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 = 530 + 1 Reorder the terms: 1 + 2x + x2 = 530 + 1 Combine like terms: 530 + 1 = 531 1 + 2x + x2 = 531 Factor a perfect square on the left side: (x + 1)(x + 1) = 531 Calculate the square root of the right side: 23.043437244 Break this problem into two subproblems by setting (x + 1) equal to 23.043437244 and -23.043437244.Subproblem 1
x + 1 = 23.043437244 Simplifying x + 1 = 23.043437244 Reorder the terms: 1 + x = 23.043437244 Solving 1 + x = 23.043437244 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 = 23.043437244 + -1 Combine like terms: 1 + -1 = 0 0 + x = 23.043437244 + -1 x = 23.043437244 + -1 Combine like terms: 23.043437244 + -1 = 22.043437244 x = 22.043437244 Simplifying x = 22.043437244Subproblem 2
x + 1 = -23.043437244 Simplifying x + 1 = -23.043437244 Reorder the terms: 1 + x = -23.043437244 Solving 1 + x = -23.043437244 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 = -23.043437244 + -1 Combine like terms: 1 + -1 = 0 0 + x = -23.043437244 + -1 x = -23.043437244 + -1 Combine like terms: -23.043437244 + -1 = -24.043437244 x = -24.043437244 Simplifying x = -24.043437244Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.043437244, -24.043437244}
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