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Simplifying x2 + -5x + -500 = x Reorder the terms: -500 + -5x + x2 = x Solving -500 + -5x + x2 = x Solving for variable 'x'. Reorder the terms: -500 + -5x + -1x + x2 = x + -1x Combine like terms: -5x + -1x = -6x -500 + -6x + x2 = x + -1x Combine like terms: x + -1x = 0 -500 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -6x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -6x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -6x + x2 = 0 + 500 -6x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -6x + x2 = 500 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 500 + 9 Reorder the terms: 9 + -6x + x2 = 500 + 9 Combine like terms: 500 + 9 = 509 9 + -6x + x2 = 509 Factor a perfect square on the left side: (x + -3)(x + -3) = 509 Calculate the square root of the right side: 22.561028345 Break this problem into two subproblems by setting (x + -3) equal to 22.561028345 and -22.561028345.Subproblem 1
x + -3 = 22.561028345 Simplifying x + -3 = 22.561028345 Reorder the terms: -3 + x = 22.561028345 Solving -3 + x = 22.561028345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 22.561028345 + 3 Combine like terms: -3 + 3 = 0 0 + x = 22.561028345 + 3 x = 22.561028345 + 3 Combine like terms: 22.561028345 + 3 = 25.561028345 x = 25.561028345 Simplifying x = 25.561028345Subproblem 2
x + -3 = -22.561028345 Simplifying x + -3 = -22.561028345 Reorder the terms: -3 + x = -22.561028345 Solving -3 + x = -22.561028345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -22.561028345 + 3 Combine like terms: -3 + 3 = 0 0 + x = -22.561028345 + 3 x = -22.561028345 + 3 Combine like terms: -22.561028345 + 3 = -19.561028345 x = -19.561028345 Simplifying x = -19.561028345Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.561028345, -19.561028345}
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