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Simplifying x2 + -500x + 6000 = 0 Reorder the terms: 6000 + -500x + x2 = 0 Solving 6000 + -500x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -500x + -6000 + x2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -500x + x2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -500x + x2 = 0 + -6000 -500x + x2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -500x + x2 = -6000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -6000 + 62500 Reorder the terms: 62500 + -500x + x2 = -6000 + 62500 Combine like terms: -6000 + 62500 = 56500 62500 + -500x + x2 = 56500 Factor a perfect square on the left side: (x + -250)(x + -250) = 56500 Calculate the square root of the right side: 237.69728648 Break this problem into two subproblems by setting (x + -250) equal to 237.69728648 and -237.69728648.Subproblem 1
x + -250 = 237.69728648 Simplifying x + -250 = 237.69728648 Reorder the terms: -250 + x = 237.69728648 Solving -250 + x = 237.69728648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 237.69728648 + 250 Combine like terms: -250 + 250 = 0 0 + x = 237.69728648 + 250 x = 237.69728648 + 250 Combine like terms: 237.69728648 + 250 = 487.69728648 x = 487.69728648 Simplifying x = 487.69728648Subproblem 2
x + -250 = -237.69728648 Simplifying x + -250 = -237.69728648 Reorder the terms: -250 + x = -237.69728648 Solving -250 + x = -237.69728648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -237.69728648 + 250 Combine like terms: -250 + 250 = 0 0 + x = -237.69728648 + 250 x = -237.69728648 + 250 Combine like terms: -237.69728648 + 250 = 12.30271352 x = 12.30271352 Simplifying x = 12.30271352Solution
The solution to the problem is based on the solutions from the subproblems. x = {487.69728648, 12.30271352}
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