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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 = 507.875939165 x = 507.875939165 Simplifying x = 507.875939165Subproblem 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 = -7.875939165 x = -7.875939165 Simplifying x = -7.875939165Solution
The solution to the problem is based on the solutions from the subproblems. x = {507.875939165, -7.875939165}
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