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Simplifying -0.0002x2 + -0.008x + 0.05 = 0 Reorder the terms: 0.05 + -0.008x + -0.0002x2 = 0 Solving 0.05 + -0.008x + -0.0002x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0002 the coefficient of the squared term: Divide each side by '-0.0002'. -250 + 40x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 40x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 40x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 40x + x2 = 0 + 250 40x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 40x + x2 = 250 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 250 + 400 Reorder the terms: 400 + 40x + x2 = 250 + 400 Combine like terms: 250 + 400 = 650 400 + 40x + x2 = 650 Factor a perfect square on the left side: (x + 20)(x + 20) = 650 Calculate the square root of the right side: 25.495097568 Break this problem into two subproblems by setting (x + 20) equal to 25.495097568 and -25.495097568.Subproblem 1
x + 20 = 25.495097568 Simplifying x + 20 = 25.495097568 Reorder the terms: 20 + x = 25.495097568 Solving 20 + x = 25.495097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 25.495097568 + -20 Combine like terms: 20 + -20 = 0 0 + x = 25.495097568 + -20 x = 25.495097568 + -20 Combine like terms: 25.495097568 + -20 = 5.495097568 x = 5.495097568 Simplifying x = 5.495097568Subproblem 2
x + 20 = -25.495097568 Simplifying x + 20 = -25.495097568 Reorder the terms: 20 + x = -25.495097568 Solving 20 + x = -25.495097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -25.495097568 + -20 Combine like terms: 20 + -20 = 0 0 + x = -25.495097568 + -20 x = -25.495097568 + -20 Combine like terms: -25.495097568 + -20 = -45.495097568 x = -45.495097568 Simplifying x = -45.495097568Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.495097568, -45.495097568}
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