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Simplifying x(x + -2) = 506 Reorder the terms: x(-2 + x) = 506 (-2 * x + x * x) = 506 (-2x + x2) = 506 Solving -2x + x2 = 506 Solving for variable 'x'. Reorder the terms: -506 + -2x + x2 = 506 + -506 Combine like terms: 506 + -506 = 0 -506 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '506' to each side of the equation. -506 + -2x + 506 + x2 = 0 + 506 Reorder the terms: -506 + 506 + -2x + x2 = 0 + 506 Combine like terms: -506 + 506 = 0 0 + -2x + x2 = 0 + 506 -2x + x2 = 0 + 506 Combine like terms: 0 + 506 = 506 -2x + x2 = 506 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 = 506 + 1 Reorder the terms: 1 + -2x + x2 = 506 + 1 Combine like terms: 506 + 1 = 507 1 + -2x + x2 = 507 Factor a perfect square on the left side: (x + -1)(x + -1) = 507 Calculate the square root of the right side: 22.516660498 Break this problem into two subproblems by setting (x + -1) equal to 22.516660498 and -22.516660498.Subproblem 1
x + -1 = 22.516660498 Simplifying x + -1 = 22.516660498 Reorder the terms: -1 + x = 22.516660498 Solving -1 + x = 22.516660498 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 = 22.516660498 + 1 Combine like terms: -1 + 1 = 0 0 + x = 22.516660498 + 1 x = 22.516660498 + 1 Combine like terms: 22.516660498 + 1 = 23.516660498 x = 23.516660498 Simplifying x = 23.516660498Subproblem 2
x + -1 = -22.516660498 Simplifying x + -1 = -22.516660498 Reorder the terms: -1 + x = -22.516660498 Solving -1 + x = -22.516660498 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 = -22.516660498 + 1 Combine like terms: -1 + 1 = 0 0 + x = -22.516660498 + 1 x = -22.516660498 + 1 Combine like terms: -22.516660498 + 1 = -21.516660498 x = -21.516660498 Simplifying x = -21.516660498Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.516660498, -21.516660498}
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