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Simplifying 0 = 800 + 40x + -0.2x2 Solving 0 = 800 + 40x + -0.2x2 Solving for variable 'x'. Combine like terms: 0 + -800 = -800 -800 + -40x + 0.2x2 = 800 + 40x + -0.2x2 + -800 + -40x + 0.2x2 Reorder the terms: -800 + -40x + 0.2x2 = 800 + -800 + 40x + -40x + -0.2x2 + 0.2x2 Combine like terms: 800 + -800 = 0 -800 + -40x + 0.2x2 = 0 + 40x + -40x + -0.2x2 + 0.2x2 -800 + -40x + 0.2x2 = 40x + -40x + -0.2x2 + 0.2x2 Combine like terms: 40x + -40x = 0 -800 + -40x + 0.2x2 = 0 + -0.2x2 + 0.2x2 -800 + -40x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -800 + -40x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -4000 + -200x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -200x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -200x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -200x + x2 = 0 + 4000 -200x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -200x + x2 = 4000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = 4000 + 10000 Reorder the terms: 10000 + -200x + x2 = 4000 + 10000 Combine like terms: 4000 + 10000 = 14000 10000 + -200x + x2 = 14000 Factor a perfect square on the left side: (x + -100)(x + -100) = 14000 Calculate the square root of the right side: 118.321595662 Break this problem into two subproblems by setting (x + -100) equal to 118.321595662 and -118.321595662.Subproblem 1
x + -100 = 118.321595662 Simplifying x + -100 = 118.321595662 Reorder the terms: -100 + x = 118.321595662 Solving -100 + x = 118.321595662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 118.321595662 + 100 Combine like terms: -100 + 100 = 0 0 + x = 118.321595662 + 100 x = 118.321595662 + 100 Combine like terms: 118.321595662 + 100 = 218.321595662 x = 218.321595662 Simplifying x = 218.321595662Subproblem 2
x + -100 = -118.321595662 Simplifying x + -100 = -118.321595662 Reorder the terms: -100 + x = -118.321595662 Solving -100 + x = -118.321595662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -118.321595662 + 100 Combine like terms: -100 + 100 = 0 0 + x = -118.321595662 + 100 x = -118.321595662 + 100 Combine like terms: -118.321595662 + 100 = -18.321595662 x = -18.321595662 Simplifying x = -18.321595662Solution
The solution to the problem is based on the solutions from the subproblems. x = {218.321595662, -18.321595662}
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