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Simplifying x2 + 2x + -576 = 0 Reorder the terms: -576 + 2x + x2 = 0 Solving -576 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 2x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 2x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 2x + x2 = 0 + 576 2x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 2x + x2 = 576 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 = 576 + 1 Reorder the terms: 1 + 2x + x2 = 576 + 1 Combine like terms: 576 + 1 = 577 1 + 2x + x2 = 577 Factor a perfect square on the left side: (x + 1)(x + 1) = 577 Calculate the square root of the right side: 24.020824299 Break this problem into two subproblems by setting (x + 1) equal to 24.020824299 and -24.020824299.Subproblem 1
x + 1 = 24.020824299 Simplifying x + 1 = 24.020824299 Reorder the terms: 1 + x = 24.020824299 Solving 1 + x = 24.020824299 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 = 24.020824299 + -1 Combine like terms: 1 + -1 = 0 0 + x = 24.020824299 + -1 x = 24.020824299 + -1 Combine like terms: 24.020824299 + -1 = 23.020824299 x = 23.020824299 Simplifying x = 23.020824299Subproblem 2
x + 1 = -24.020824299 Simplifying x + 1 = -24.020824299 Reorder the terms: 1 + x = -24.020824299 Solving 1 + x = -24.020824299 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 = -24.020824299 + -1 Combine like terms: 1 + -1 = 0 0 + x = -24.020824299 + -1 x = -24.020824299 + -1 Combine like terms: -24.020824299 + -1 = -25.020824299 x = -25.020824299 Simplifying x = -25.020824299Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.020824299, -25.020824299}
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