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Simplifying 95x + -1x2 + -20 = 0 Reorder the terms: -20 + 95x + -1x2 = 0 Solving -20 + 95x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -95x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -95x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -95x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -95x + x2 = 0 + -20 -95x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -95x + x2 = -20 The x term is -95x. Take half its coefficient (-47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. -95x + 2256.25 + x2 = -20 + 2256.25 Reorder the terms: 2256.25 + -95x + x2 = -20 + 2256.25 Combine like terms: -20 + 2256.25 = 2236.25 2256.25 + -95x + x2 = 2236.25 Factor a perfect square on the left side: (x + -47.5)(x + -47.5) = 2236.25 Calculate the square root of the right side: 47.289005065 Break this problem into two subproblems by setting (x + -47.5) equal to 47.289005065 and -47.289005065.Subproblem 1
x + -47.5 = 47.289005065 Simplifying x + -47.5 = 47.289005065 Reorder the terms: -47.5 + x = 47.289005065 Solving -47.5 + x = 47.289005065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = 47.289005065 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = 47.289005065 + 47.5 x = 47.289005065 + 47.5 Combine like terms: 47.289005065 + 47.5 = 94.789005065 x = 94.789005065 Simplifying x = 94.789005065Subproblem 2
x + -47.5 = -47.289005065 Simplifying x + -47.5 = -47.289005065 Reorder the terms: -47.5 + x = -47.289005065 Solving -47.5 + x = -47.289005065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = -47.289005065 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = -47.289005065 + 47.5 x = -47.289005065 + 47.5 Combine like terms: -47.289005065 + 47.5 = 0.210994935 x = 0.210994935 Simplifying x = 0.210994935Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.789005065, 0.210994935}
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