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Simplifying 0.05x2 + 20x + 320 = 0 Reorder the terms: 320 + 20x + 0.05x2 = 0 Solving 320 + 20x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 6400 + 400x + x2 = 0 Move the constant term to the right: Add '-6400' to each side of the equation. 6400 + 400x + -6400 + x2 = 0 + -6400 Reorder the terms: 6400 + -6400 + 400x + x2 = 0 + -6400 Combine like terms: 6400 + -6400 = 0 0 + 400x + x2 = 0 + -6400 400x + x2 = 0 + -6400 Combine like terms: 0 + -6400 = -6400 400x + x2 = -6400 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 = -6400 + 40000 Reorder the terms: 40000 + 400x + x2 = -6400 + 40000 Combine like terms: -6400 + 40000 = 33600 40000 + 400x + x2 = 33600 Factor a perfect square on the left side: (x + 200)(x + 200) = 33600 Calculate the square root of the right side: 183.303027798 Break this problem into two subproblems by setting (x + 200) equal to 183.303027798 and -183.303027798.Subproblem 1
x + 200 = 183.303027798 Simplifying x + 200 = 183.303027798 Reorder the terms: 200 + x = 183.303027798 Solving 200 + x = 183.303027798 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 = 183.303027798 + -200 Combine like terms: 200 + -200 = 0 0 + x = 183.303027798 + -200 x = 183.303027798 + -200 Combine like terms: 183.303027798 + -200 = -16.696972202 x = -16.696972202 Simplifying x = -16.696972202Subproblem 2
x + 200 = -183.303027798 Simplifying x + 200 = -183.303027798 Reorder the terms: 200 + x = -183.303027798 Solving 200 + x = -183.303027798 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 = -183.303027798 + -200 Combine like terms: 200 + -200 = 0 0 + x = -183.303027798 + -200 x = -183.303027798 + -200 Combine like terms: -183.303027798 + -200 = -383.303027798 x = -383.303027798 Simplifying x = -383.303027798Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.696972202, -383.303027798}
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