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Simplifying x2 + -4x + -516 = 0 Reorder the terms: -516 + -4x + x2 = 0 Solving -516 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '516' to each side of the equation. -516 + -4x + 516 + x2 = 0 + 516 Reorder the terms: -516 + 516 + -4x + x2 = 0 + 516 Combine like terms: -516 + 516 = 0 0 + -4x + x2 = 0 + 516 -4x + x2 = 0 + 516 Combine like terms: 0 + 516 = 516 -4x + x2 = 516 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 516 + 4 Reorder the terms: 4 + -4x + x2 = 516 + 4 Combine like terms: 516 + 4 = 520 4 + -4x + x2 = 520 Factor a perfect square on the left side: (x + -2)(x + -2) = 520 Calculate the square root of the right side: 22.803508502 Break this problem into two subproblems by setting (x + -2) equal to 22.803508502 and -22.803508502.Subproblem 1
x + -2 = 22.803508502 Simplifying x + -2 = 22.803508502 Reorder the terms: -2 + x = 22.803508502 Solving -2 + x = 22.803508502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 22.803508502 + 2 Combine like terms: -2 + 2 = 0 0 + x = 22.803508502 + 2 x = 22.803508502 + 2 Combine like terms: 22.803508502 + 2 = 24.803508502 x = 24.803508502 Simplifying x = 24.803508502Subproblem 2
x + -2 = -22.803508502 Simplifying x + -2 = -22.803508502 Reorder the terms: -2 + x = -22.803508502 Solving -2 + x = -22.803508502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -22.803508502 + 2 Combine like terms: -2 + 2 = 0 0 + x = -22.803508502 + 2 x = -22.803508502 + 2 Combine like terms: -22.803508502 + 2 = -20.803508502 x = -20.803508502 Simplifying x = -20.803508502Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.803508502, -20.803508502}
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