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Simplifying -0.2x2 + 115x + -9500 = 0 Reorder the terms: -9500 + 115x + -0.2x2 = 0 Solving -9500 + 115x + -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'. 47500 + -575x + x2 = 0 Move the constant term to the right: Add '-47500' to each side of the equation. 47500 + -575x + -47500 + x2 = 0 + -47500 Reorder the terms: 47500 + -47500 + -575x + x2 = 0 + -47500 Combine like terms: 47500 + -47500 = 0 0 + -575x + x2 = 0 + -47500 -575x + x2 = 0 + -47500 Combine like terms: 0 + -47500 = -47500 -575x + x2 = -47500 The x term is -575x. Take half its coefficient (-287.5). Square it (82656.25) and add it to both sides. Add '82656.25' to each side of the equation. -575x + 82656.25 + x2 = -47500 + 82656.25 Reorder the terms: 82656.25 + -575x + x2 = -47500 + 82656.25 Combine like terms: -47500 + 82656.25 = 35156.25 82656.25 + -575x + x2 = 35156.25 Factor a perfect square on the left side: (x + -287.5)(x + -287.5) = 35156.25 Calculate the square root of the right side: 187.5 Break this problem into two subproblems by setting (x + -287.5) equal to 187.5 and -187.5.Subproblem 1
x + -287.5 = 187.5 Simplifying x + -287.5 = 187.5 Reorder the terms: -287.5 + x = 187.5 Solving -287.5 + x = 187.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '287.5' to each side of the equation. -287.5 + 287.5 + x = 187.5 + 287.5 Combine like terms: -287.5 + 287.5 = 0.0 0.0 + x = 187.5 + 287.5 x = 187.5 + 287.5 Combine like terms: 187.5 + 287.5 = 475 x = 475 Simplifying x = 475Subproblem 2
x + -287.5 = -187.5 Simplifying x + -287.5 = -187.5 Reorder the terms: -287.5 + x = -187.5 Solving -287.5 + x = -187.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '287.5' to each side of the equation. -287.5 + 287.5 + x = -187.5 + 287.5 Combine like terms: -287.5 + 287.5 = 0.0 0.0 + x = -187.5 + 287.5 x = -187.5 + 287.5 Combine like terms: -187.5 + 287.5 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {475, 100}
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