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Simplifying 18 = 500x + -5x2 Solving 18 = 500x + -5x2 Solving for variable 'x'. Reorder the terms: 18 + -500x + 5x2 = 500x + -500x + -5x2 + 5x2 Combine like terms: 500x + -500x = 0 18 + -500x + 5x2 = 0 + -5x2 + 5x2 18 + -500x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 18 + -500x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -100x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -100x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -100x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -100x + x2 = 0 + -3.6 -100x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -100x + x2 = -3.6 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 = -3.6 + 2500 Reorder the terms: 2500 + -100x + x2 = -3.6 + 2500 Combine like terms: -3.6 + 2500 = 2496.4 2500 + -100x + x2 = 2496.4 Factor a perfect square on the left side: (x + -50)(x + -50) = 2496.4 Calculate the square root of the right side: 49.963987031 Break this problem into two subproblems by setting (x + -50) equal to 49.963987031 and -49.963987031.Subproblem 1
x + -50 = 49.963987031 Simplifying x + -50 = 49.963987031 Reorder the terms: -50 + x = 49.963987031 Solving -50 + x = 49.963987031 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 = 49.963987031 + 50 Combine like terms: -50 + 50 = 0 0 + x = 49.963987031 + 50 x = 49.963987031 + 50 Combine like terms: 49.963987031 + 50 = 99.963987031 x = 99.963987031 Simplifying x = 99.963987031Subproblem 2
x + -50 = -49.963987031 Simplifying x + -50 = -49.963987031 Reorder the terms: -50 + x = -49.963987031 Solving -50 + x = -49.963987031 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 = -49.963987031 + 50 Combine like terms: -50 + 50 = 0 0 + x = -49.963987031 + 50 x = -49.963987031 + 50 Combine like terms: -49.963987031 + 50 = 0.036012969 x = 0.036012969 Simplifying x = 0.036012969Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.963987031, 0.036012969}
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