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Simplifying -0.01x2 + -0.2x + 3 = 0 Reorder the terms: 3 + -0.2x + -0.01x2 = 0 Solving 3 + -0.2x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -300 + 20x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 20x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 20x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 20x + x2 = 0 + 300 20x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 20x + x2 = 300 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 = 300 + 100 Reorder the terms: 100 + 20x + x2 = 300 + 100 Combine like terms: 300 + 100 = 400 100 + 20x + x2 = 400 Factor a perfect square on the left side: (x + 10)(x + 10) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (x + 10) equal to 20 and -20.Subproblem 1
x + 10 = 20 Simplifying x + 10 = 20 Reorder the terms: 10 + x = 20 Solving 10 + x = 20 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 = 20 + -10 Combine like terms: 10 + -10 = 0 0 + x = 20 + -10 x = 20 + -10 Combine like terms: 20 + -10 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 10 = -20 Simplifying x + 10 = -20 Reorder the terms: 10 + x = -20 Solving 10 + x = -20 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 = -20 + -10 Combine like terms: 10 + -10 = 0 0 + x = -20 + -10 x = -20 + -10 Combine like terms: -20 + -10 = -30 x = -30 Simplifying x = -30Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -30}
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