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Simplifying x2 + -10x + -520 = 0 Reorder the terms: -520 + -10x + x2 = 0 Solving -520 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + -10x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + -10x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + -10x + x2 = 0 + 520 -10x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 -10x + x2 = 520 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 520 + 25 Reorder the terms: 25 + -10x + x2 = 520 + 25 Combine like terms: 520 + 25 = 545 25 + -10x + x2 = 545 Factor a perfect square on the left side: (x + -5)(x + -5) = 545 Calculate the square root of the right side: 23.34523506 Break this problem into two subproblems by setting (x + -5) equal to 23.34523506 and -23.34523506.Subproblem 1
x + -5 = 23.34523506 Simplifying x + -5 = 23.34523506 Reorder the terms: -5 + x = 23.34523506 Solving -5 + x = 23.34523506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 23.34523506 + 5 Combine like terms: -5 + 5 = 0 0 + x = 23.34523506 + 5 x = 23.34523506 + 5 Combine like terms: 23.34523506 + 5 = 28.34523506 x = 28.34523506 Simplifying x = 28.34523506Subproblem 2
x + -5 = -23.34523506 Simplifying x + -5 = -23.34523506 Reorder the terms: -5 + x = -23.34523506 Solving -5 + x = -23.34523506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -23.34523506 + 5 Combine like terms: -5 + 5 = 0 0 + x = -23.34523506 + 5 x = -23.34523506 + 5 Combine like terms: -23.34523506 + 5 = -18.34523506 x = -18.34523506 Simplifying x = -18.34523506Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.34523506, -18.34523506}
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