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Simplifying 100x + -1x2 = 500 Solving 100x + -1x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 100x + -1x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 500 + -100x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -100x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -100x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -100x + x2 = 0 + -500 -100x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -100x + x2 = -500 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -500 + 2500 Reorder the terms: 2500 + -100x + x2 = -500 + 2500 Combine like terms: -500 + 2500 = 2000 2500 + -100x + x2 = 2000 Factor a perfect square on the left side: (x + -50)(x + -50) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (x + -50) equal to 44.72135955 and -44.72135955.Subproblem 1
x + -50 = 44.72135955 Simplifying x + -50 = 44.72135955 Reorder the terms: -50 + x = 44.72135955 Solving -50 + x = 44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 44.72135955 + 50 Combine like terms: -50 + 50 = 0 0 + x = 44.72135955 + 50 x = 44.72135955 + 50 Combine like terms: 44.72135955 + 50 = 94.72135955 x = 94.72135955 Simplifying x = 94.72135955Subproblem 2
x + -50 = -44.72135955 Simplifying x + -50 = -44.72135955 Reorder the terms: -50 + x = -44.72135955 Solving -50 + x = -44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -44.72135955 + 50 Combine like terms: -50 + 50 = 0 0 + x = -44.72135955 + 50 x = -44.72135955 + 50 Combine like terms: -44.72135955 + 50 = 5.27864045 x = 5.27864045 Simplifying x = 5.27864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.72135955, 5.27864045}
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