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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 = 4900 2500 + 100x + x2 = 4900 Factor a perfect square on the left side: (x + 50)(x + 50) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (x + 50) equal to 70 and -70.Subproblem 1
x + 50 = 70 Simplifying x + 50 = 70 Reorder the terms: 50 + x = 70 Solving 50 + x = 70 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 = 70 + -50 Combine like terms: 50 + -50 = 0 0 + x = 70 + -50 x = 70 + -50 Combine like terms: 70 + -50 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 50 = -70 Simplifying x + 50 = -70 Reorder the terms: 50 + x = -70 Solving 50 + x = -70 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 = -70 + -50 Combine like terms: 50 + -50 = 0 0 + x = -70 + -50 x = -70 + -50 Combine like terms: -70 + -50 = -120 x = -120 Simplifying x = -120Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -120}
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