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Simplifying 0.25x2 + 11x + 120 = 0 Reorder the terms: 120 + 11x + 0.25x2 = 0 Solving 120 + 11x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 480 + 44x + x2 = 0 Move the constant term to the right: Add '-480' to each side of the equation. 480 + 44x + -480 + x2 = 0 + -480 Reorder the terms: 480 + -480 + 44x + x2 = 0 + -480 Combine like terms: 480 + -480 = 0 0 + 44x + x2 = 0 + -480 44x + x2 = 0 + -480 Combine like terms: 0 + -480 = -480 44x + x2 = -480 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = -480 + 484 Reorder the terms: 484 + 44x + x2 = -480 + 484 Combine like terms: -480 + 484 = 4 484 + 44x + x2 = 4 Factor a perfect square on the left side: (x + 22)(x + 22) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 22) equal to 2 and -2.Subproblem 1
x + 22 = 2 Simplifying x + 22 = 2 Reorder the terms: 22 + x = 2 Solving 22 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 2 + -22 Combine like terms: 22 + -22 = 0 0 + x = 2 + -22 x = 2 + -22 Combine like terms: 2 + -22 = -20 x = -20 Simplifying x = -20Subproblem 2
x + 22 = -2 Simplifying x + 22 = -2 Reorder the terms: 22 + x = -2 Solving 22 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -2 + -22 Combine like terms: 22 + -22 = 0 0 + x = -2 + -22 x = -2 + -22 Combine like terms: -2 + -22 = -24 x = -24 Simplifying x = -24Solution
The solution to the problem is based on the solutions from the subproblems. x = {-20, -24}
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