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Simplifying -0.2x2 + 20x + -320 = 0 Reorder the terms: -320 + 20x + -0.2x2 = 0 Solving -320 + 20x + -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'. 1600 + -100x + x2 = 0 Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -100x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -100x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -100x + x2 = 0 + -1600 -100x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -100x + x2 = -1600 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1600 + 2500 Reorder the terms: 2500 + -100x + x2 = -1600 + 2500 Combine like terms: -1600 + 2500 = 900 2500 + -100x + x2 = 900 Factor a perfect square on the left side: (x + -50)(x + -50) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + -50) equal to 30 and -30.Subproblem 1
x + -50 = 30 Simplifying x + -50 = 30 Reorder the terms: -50 + x = 30 Solving -50 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 30 + 50 Combine like terms: -50 + 50 = 0 0 + x = 30 + 50 x = 30 + 50 Combine like terms: 30 + 50 = 80 x = 80 Simplifying x = 80Subproblem 2
x + -50 = -30 Simplifying x + -50 = -30 Reorder the terms: -50 + x = -30 Solving -50 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -30 + 50 Combine like terms: -50 + 50 = 0 0 + x = -30 + 50 x = -30 + 50 Combine like terms: -30 + 50 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {80, 20}
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