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Simplifying 0.2x2 + 80x = 1500 Reorder the terms: 80x + 0.2x2 = 1500 Solving 80x + 0.2x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 80x + 0.2x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 80x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -7500 + 400x + x2 = 0 Move the constant term to the right: Add '7500' to each side of the equation. -7500 + 400x + 7500 + x2 = 0 + 7500 Reorder the terms: -7500 + 7500 + 400x + x2 = 0 + 7500 Combine like terms: -7500 + 7500 = 0 0 + 400x + x2 = 0 + 7500 400x + x2 = 0 + 7500 Combine like terms: 0 + 7500 = 7500 400x + x2 = 7500 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = 7500 + 40000 Reorder the terms: 40000 + 400x + x2 = 7500 + 40000 Combine like terms: 7500 + 40000 = 47500 40000 + 400x + x2 = 47500 Factor a perfect square on the left side: (x + 200)(x + 200) = 47500 Calculate the square root of the right side: 217.944947177 Break this problem into two subproblems by setting (x + 200) equal to 217.944947177 and -217.944947177.Subproblem 1
x + 200 = 217.944947177 Simplifying x + 200 = 217.944947177 Reorder the terms: 200 + x = 217.944947177 Solving 200 + x = 217.944947177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 217.944947177 + -200 Combine like terms: 200 + -200 = 0 0 + x = 217.944947177 + -200 x = 217.944947177 + -200 Combine like terms: 217.944947177 + -200 = 17.944947177 x = 17.944947177 Simplifying x = 17.944947177Subproblem 2
x + 200 = -217.944947177 Simplifying x + 200 = -217.944947177 Reorder the terms: 200 + x = -217.944947177 Solving 200 + x = -217.944947177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -217.944947177 + -200 Combine like terms: 200 + -200 = 0 0 + x = -217.944947177 + -200 x = -217.944947177 + -200 Combine like terms: -217.944947177 + -200 = -417.944947177 x = -417.944947177 Simplifying x = -417.944947177Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.944947177, -417.944947177}
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