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Simplifying x(x + -500) = 550 Reorder the terms: x(-500 + x) = 550 (-500 * x + x * x) = 550 (-500x + x2) = 550 Solving -500x + x2 = 550 Solving for variable 'x'. Reorder the terms: -550 + -500x + x2 = 550 + -550 Combine like terms: 550 + -550 = 0 -550 + -500x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '550' to each side of the equation. -550 + -500x + 550 + x2 = 0 + 550 Reorder the terms: -550 + 550 + -500x + x2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + -500x + x2 = 0 + 550 -500x + x2 = 0 + 550 Combine like terms: 0 + 550 = 550 -500x + x2 = 550 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 = 550 + 62500 Reorder the terms: 62500 + -500x + x2 = 550 + 62500 Combine like terms: 550 + 62500 = 63050 62500 + -500x + x2 = 63050 Factor a perfect square on the left side: (x + -250)(x + -250) = 63050 Calculate the square root of the right side: 251.09759059 Break this problem into two subproblems by setting (x + -250) equal to 251.09759059 and -251.09759059.Subproblem 1
x + -250 = 251.09759059 Simplifying x + -250 = 251.09759059 Reorder the terms: -250 + x = 251.09759059 Solving -250 + x = 251.09759059 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 = 251.09759059 + 250 Combine like terms: -250 + 250 = 0 0 + x = 251.09759059 + 250 x = 251.09759059 + 250 Combine like terms: 251.09759059 + 250 = 501.09759059 x = 501.09759059 Simplifying x = 501.09759059Subproblem 2
x + -250 = -251.09759059 Simplifying x + -250 = -251.09759059 Reorder the terms: -250 + x = -251.09759059 Solving -250 + x = -251.09759059 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 = -251.09759059 + 250 Combine like terms: -250 + 250 = 0 0 + x = -251.09759059 + 250 x = -251.09759059 + 250 Combine like terms: -251.09759059 + 250 = -1.09759059 x = -1.09759059 Simplifying x = -1.09759059Solution
The solution to the problem is based on the solutions from the subproblems. x = {501.09759059, -1.09759059}
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