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Simplifying 0 = -0.01x2 + -0.2x + 8 Reorder the terms: 0 = 8 + -0.2x + -0.01x2 Solving 0 = 8 + -0.2x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 0.2x + 0.01x2 = 8 + -0.2x + -0.01x2 + -8 + 0.2x + 0.01x2 Reorder the terms: -8 + 0.2x + 0.01x2 = 8 + -8 + -0.2x + 0.2x + -0.01x2 + 0.01x2 Combine like terms: 8 + -8 = 0 -8 + 0.2x + 0.01x2 = 0 + -0.2x + 0.2x + -0.01x2 + 0.01x2 -8 + 0.2x + 0.01x2 = -0.2x + 0.2x + -0.01x2 + 0.01x2 Combine like terms: -0.2x + 0.2x = 0.0 -8 + 0.2x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -8 + 0.2x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -8 + 0.2x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -800 + 20x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + 20x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 20x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 20x + x2 = 0 + 800 20x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 20x + x2 = 800 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 800 + 100 Reorder the terms: 100 + 20x + x2 = 800 + 100 Combine like terms: 800 + 100 = 900 100 + 20x + x2 = 900 Factor a perfect square on the left side: (x + 10)(x + 10) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + 10) equal to 30 and -30.Subproblem 1
x + 10 = 30 Simplifying x + 10 = 30 Reorder the terms: 10 + x = 30 Solving 10 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 30 + -10 Combine like terms: 10 + -10 = 0 0 + x = 30 + -10 x = 30 + -10 Combine like terms: 30 + -10 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 10 = -30 Simplifying x + 10 = -30 Reorder the terms: 10 + x = -30 Solving 10 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -30 + -10 Combine like terms: 10 + -10 = 0 0 + x = -30 + -10 x = -30 + -10 Combine like terms: -30 + -10 = -40 x = -40 Simplifying x = -40Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -40}
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