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Simplifying 0 = -100 + 20x + 0.25x2 Solving 0 = -100 + 20x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + -20x + -0.25x2 = -100 + 20x + 0.25x2 + 100 + -20x + -0.25x2 Reorder the terms: 100 + -20x + -0.25x2 = -100 + 100 + 20x + -20x + 0.25x2 + -0.25x2 Combine like terms: -100 + 100 = 0 100 + -20x + -0.25x2 = 0 + 20x + -20x + 0.25x2 + -0.25x2 100 + -20x + -0.25x2 = 20x + -20x + 0.25x2 + -0.25x2 Combine like terms: 20x + -20x = 0 100 + -20x + -0.25x2 = 0 + 0.25x2 + -0.25x2 100 + -20x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 100 + -20x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -400 + 80x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 80x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 80x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 80x + x2 = 0 + 400 80x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 80x + x2 = 400 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 400 + 1600 Reorder the terms: 1600 + 80x + x2 = 400 + 1600 Combine like terms: 400 + 1600 = 2000 1600 + 80x + x2 = 2000 Factor a perfect square on the left side: (x + 40)(x + 40) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (x + 40) equal to 44.72135955 and -44.72135955.Subproblem 1
x + 40 = 44.72135955 Simplifying x + 40 = 44.72135955 Reorder the terms: 40 + x = 44.72135955 Solving 40 + x = 44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 44.72135955 + -40 Combine like terms: 40 + -40 = 0 0 + x = 44.72135955 + -40 x = 44.72135955 + -40 Combine like terms: 44.72135955 + -40 = 4.72135955 x = 4.72135955 Simplifying x = 4.72135955Subproblem 2
x + 40 = -44.72135955 Simplifying x + 40 = -44.72135955 Reorder the terms: 40 + x = -44.72135955 Solving 40 + x = -44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -44.72135955 + -40 Combine like terms: 40 + -40 = 0 0 + x = -44.72135955 + -40 x = -44.72135955 + -40 Combine like terms: -44.72135955 + -40 = -84.72135955 x = -84.72135955 Simplifying x = -84.72135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.72135955, -84.72135955}
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