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Simplifying -0.1x2 + 50x = 6250 Reorder the terms: 50x + -0.1x2 = 6250 Solving 50x + -0.1x2 = 6250 Solving for variable 'x'. Reorder the terms: -6250 + 50x + -0.1x2 = 6250 + -6250 Combine like terms: 6250 + -6250 = 0 -6250 + 50x + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 62500 + -500x + x2 = 0 Move the constant term to the right: Add '-62500' to each side of the equation. 62500 + -500x + -62500 + x2 = 0 + -62500 Reorder the terms: 62500 + -62500 + -500x + x2 = 0 + -62500 Combine like terms: 62500 + -62500 = 0 0 + -500x + x2 = 0 + -62500 -500x + x2 = 0 + -62500 Combine like terms: 0 + -62500 = -62500 -500x + x2 = -62500 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 = -62500 + 62500 Reorder the terms: 62500 + -500x + x2 = -62500 + 62500 Combine like terms: -62500 + 62500 = 0 62500 + -500x + x2 = 0 Factor a perfect square on the left side: (x + -250)(x + -250) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -250) equal to 0 and 0.Subproblem 1
x + -250 = 0 Simplifying x + -250 = 0 Reorder the terms: -250 + x = 0 Solving -250 + x = 0 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 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + x = 0 + 250 x = 0 + 250 Combine like terms: 0 + 250 = 250 x = 250 Simplifying x = 250Subproblem 2
x + -250 = 0 Simplifying x + -250 = 0 Reorder the terms: -250 + x = 0 Solving -250 + x = 0 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 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + x = 0 + 250 x = 0 + 250 Combine like terms: 0 + 250 = 250 x = 250 Simplifying x = 250Solution
The solution to the problem is based on the solutions from the subproblems. x = {250, 250}
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