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Simplifying x2 + -44x + 120 = -30 + 11x Reorder the terms: 120 + -44x + x2 = -30 + 11x Solving 120 + -44x + x2 = -30 + 11x Solving for variable 'x'. Reorder the terms: 120 + 30 + -44x + -11x + x2 = -30 + 11x + 30 + -11x Combine like terms: 120 + 30 = 150 150 + -44x + -11x + x2 = -30 + 11x + 30 + -11x Combine like terms: -44x + -11x = -55x 150 + -55x + x2 = -30 + 11x + 30 + -11x Reorder the terms: 150 + -55x + x2 = -30 + 30 + 11x + -11x Combine like terms: -30 + 30 = 0 150 + -55x + x2 = 0 + 11x + -11x 150 + -55x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 150 + -55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -55x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -55x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -55x + x2 = 0 + -150 -55x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -55x + x2 = -150 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -150 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -150 + 756.25 Combine like terms: -150 + 756.25 = 606.25 756.25 + -55x + x2 = 606.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + -27.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + -27.5 = 24.622144504 Simplifying x + -27.5 = 24.622144504 Reorder the terms: -27.5 + x = 24.622144504 Solving -27.5 + x = 24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 24.622144504 + 27.5 x = 24.622144504 + 27.5 Combine like terms: 24.622144504 + 27.5 = 52.122144504 x = 52.122144504 Simplifying x = 52.122144504Subproblem 2
x + -27.5 = -24.622144504 Simplifying x + -27.5 = -24.622144504 Reorder the terms: -27.5 + x = -24.622144504 Solving -27.5 + x = -24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -24.622144504 + 27.5 x = -24.622144504 + 27.5 Combine like terms: -24.622144504 + 27.5 = 2.877855496 x = 2.877855496 Simplifying x = 2.877855496Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.122144504, 2.877855496}
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