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Simplifying -1500 + 100x + -0.2x2 = 0 Solving -1500 + 100x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 7500 + -500x + x2 = 0 Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -500x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -500x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -500x + x2 = 0 + -7500 -500x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -500x + x2 = -7500 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 = -7500 + 62500 Reorder the terms: 62500 + -500x + x2 = -7500 + 62500 Combine like terms: -7500 + 62500 = 55000 62500 + -500x + x2 = 55000 Factor a perfect square on the left side: (x + -250)(x + -250) = 55000 Calculate the square root of the right side: 234.520787991 Break this problem into two subproblems by setting (x + -250) equal to 234.520787991 and -234.520787991.Subproblem 1
x + -250 = 234.520787991 Simplifying x + -250 = 234.520787991 Reorder the terms: -250 + x = 234.520787991 Solving -250 + x = 234.520787991 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 = 234.520787991 + 250 Combine like terms: -250 + 250 = 0 0 + x = 234.520787991 + 250 x = 234.520787991 + 250 Combine like terms: 234.520787991 + 250 = 484.520787991 x = 484.520787991 Simplifying x = 484.520787991Subproblem 2
x + -250 = -234.520787991 Simplifying x + -250 = -234.520787991 Reorder the terms: -250 + x = -234.520787991 Solving -250 + x = -234.520787991 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 = -234.520787991 + 250 Combine like terms: -250 + 250 = 0 0 + x = -234.520787991 + 250 x = -234.520787991 + 250 Combine like terms: -234.520787991 + 250 = 15.479212009 x = 15.479212009 Simplifying x = 15.479212009Solution
The solution to the problem is based on the solutions from the subproblems. x = {484.520787991, 15.479212009}
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