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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 = 58500 62500 + -500x + x2 = 58500 Factor a perfect square on the left side: (x + -250)(x + -250) = 58500 Calculate the square root of the right side: 241.867732449 Break this problem into two subproblems by setting (x + -250) equal to 241.867732449 and -241.867732449.Subproblem 1
x + -250 = 241.867732449 Simplifying x + -250 = 241.867732449 Reorder the terms: -250 + x = 241.867732449 Solving -250 + x = 241.867732449 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 = 241.867732449 + 250 Combine like terms: -250 + 250 = 0 0 + x = 241.867732449 + 250 x = 241.867732449 + 250 Combine like terms: 241.867732449 + 250 = 491.867732449 x = 491.867732449 Simplifying x = 491.867732449Subproblem 2
x + -250 = -241.867732449 Simplifying x + -250 = -241.867732449 Reorder the terms: -250 + x = -241.867732449 Solving -250 + x = -241.867732449 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 = -241.867732449 + 250 Combine like terms: -250 + 250 = 0 0 + x = -241.867732449 + 250 x = -241.867732449 + 250 Combine like terms: -241.867732449 + 250 = 8.132267551 x = 8.132267551 Simplifying x = 8.132267551Solution
The solution to the problem is based on the solutions from the subproblems. x = {491.867732449, 8.132267551}
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