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Simplifying 0.2x2 + -20x + 480 = 0 Reorder the terms: 480 + -20x + 0.2x2 = 0 Solving 480 + -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'. 2400 + -100x + x2 = 0 Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + -100x + -2400 + x2 = 0 + -2400 Reorder the terms: 2400 + -2400 + -100x + x2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + -100x + x2 = 0 + -2400 -100x + x2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 -100x + x2 = -2400 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 = -2400 + 2500 Reorder the terms: 2500 + -100x + x2 = -2400 + 2500 Combine like terms: -2400 + 2500 = 100 2500 + -100x + x2 = 100 Factor a perfect square on the left side: (x + -50)(x + -50) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -50) equal to 10 and -10.Subproblem 1
x + -50 = 10 Simplifying x + -50 = 10 Reorder the terms: -50 + x = 10 Solving -50 + x = 10 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 = 10 + 50 Combine like terms: -50 + 50 = 0 0 + x = 10 + 50 x = 10 + 50 Combine like terms: 10 + 50 = 60 x = 60 Simplifying x = 60Subproblem 2
x + -50 = -10 Simplifying x + -50 = -10 Reorder the terms: -50 + x = -10 Solving -50 + x = -10 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 = -10 + 50 Combine like terms: -50 + 50 = 0 0 + x = -10 + 50 x = -10 + 50 Combine like terms: -10 + 50 = 40 x = 40 Simplifying x = 40Solution
The solution to the problem is based on the solutions from the subproblems. x = {60, 40}
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