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Simplifying -0.2x2 + -100x + 800 = 0 Reorder the terms: 800 + -100x + -0.2x2 = 0 Solving 800 + -100x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -4000 + 500x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 500x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 500x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 500x + x2 = 0 + 4000 500x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 500x + x2 = 4000 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 4000 + 62500 Reorder the terms: 62500 + 500x + x2 = 4000 + 62500 Combine like terms: 4000 + 62500 = 66500 62500 + 500x + x2 = 66500 Factor a perfect square on the left side: (x + 250)(x + 250) = 66500 Calculate the square root of the right side: 257.875939165 Break this problem into two subproblems by setting (x + 250) equal to 257.875939165 and -257.875939165.Subproblem 1
x + 250 = 257.875939165 Simplifying x + 250 = 257.875939165 Reorder the terms: 250 + x = 257.875939165 Solving 250 + x = 257.875939165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 257.875939165 + -250 Combine like terms: 250 + -250 = 0 0 + x = 257.875939165 + -250 x = 257.875939165 + -250 Combine like terms: 257.875939165 + -250 = 7.875939165 x = 7.875939165 Simplifying x = 7.875939165Subproblem 2
x + 250 = -257.875939165 Simplifying x + 250 = -257.875939165 Reorder the terms: 250 + x = -257.875939165 Solving 250 + x = -257.875939165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -257.875939165 + -250 Combine like terms: 250 + -250 = 0 0 + x = -257.875939165 + -250 x = -257.875939165 + -250 Combine like terms: -257.875939165 + -250 = -507.875939165 x = -507.875939165 Simplifying x = -507.875939165Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.875939165, -507.875939165}
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