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Simplifying 5x2 + -44x + 120 = -3 + 11x Reorder the terms: 120 + -44x + 5x2 = -3 + 11x Solving 120 + -44x + 5x2 = -3 + 11x Solving for variable 'x'. Reorder the terms: 120 + 3 + -44x + -11x + 5x2 = -3 + 11x + 3 + -11x Combine like terms: 120 + 3 = 123 123 + -44x + -11x + 5x2 = -3 + 11x + 3 + -11x Combine like terms: -44x + -11x = -55x 123 + -55x + 5x2 = -3 + 11x + 3 + -11x Reorder the terms: 123 + -55x + 5x2 = -3 + 3 + 11x + -11x Combine like terms: -3 + 3 = 0 123 + -55x + 5x2 = 0 + 11x + -11x 123 + -55x + 5x2 = 11x + -11x Combine like terms: 11x + -11x = 0 123 + -55x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 24.6 + -11x + x2 = 0 Move the constant term to the right: Add '-24.6' to each side of the equation. 24.6 + -11x + -24.6 + x2 = 0 + -24.6 Reorder the terms: 24.6 + -24.6 + -11x + x2 = 0 + -24.6 Combine like terms: 24.6 + -24.6 = 0.0 0.0 + -11x + x2 = 0 + -24.6 -11x + x2 = 0 + -24.6 Combine like terms: 0 + -24.6 = -24.6 -11x + x2 = -24.6 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -24.6 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -24.6 + 30.25 Combine like terms: -24.6 + 30.25 = 5.65 30.25 + -11x + x2 = 5.65 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 5.65 Calculate the square root of the right side: 2.376972865 Break this problem into two subproblems by setting (x + -5.5) equal to 2.376972865 and -2.376972865.Subproblem 1
x + -5.5 = 2.376972865 Simplifying x + -5.5 = 2.376972865 Reorder the terms: -5.5 + x = 2.376972865 Solving -5.5 + x = 2.376972865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.376972865 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.376972865 + 5.5 x = 2.376972865 + 5.5 Combine like terms: 2.376972865 + 5.5 = 7.876972865 x = 7.876972865 Simplifying x = 7.876972865Subproblem 2
x + -5.5 = -2.376972865 Simplifying x + -5.5 = -2.376972865 Reorder the terms: -5.5 + x = -2.376972865 Solving -5.5 + x = -2.376972865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.376972865 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.376972865 + 5.5 x = -2.376972865 + 5.5 Combine like terms: -2.376972865 + 5.5 = 3.123027135 x = 3.123027135 Simplifying x = 3.123027135Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.876972865, 3.123027135}
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