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Simplifying 4x2 + 44x + -122 = 0 Reorder the terms: -122 + 44x + 4x2 = 0 Solving -122 + 44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + 22x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + 22x + 2x2)' equal to zero and attempt to solve: Simplifying -61 + 22x + 2x2 = 0 Solving -61 + 22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30.5 + 11x + x2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + 11x + 30.5 + x2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + 11x + x2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + 11x + x2 = 0 + 30.5 11x + x2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 11x + x2 = 30.5 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 = 30.5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 30.5 + 30.25 Combine like terms: 30.5 + 30.25 = 60.75 30.25 + 11x + x2 = 60.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 60.75 Calculate the square root of the right side: 7.794228634 Break this problem into two subproblems by setting (x + 5.5) equal to 7.794228634 and -7.794228634.Subproblem 1
x + 5.5 = 7.794228634 Simplifying x + 5.5 = 7.794228634 Reorder the terms: 5.5 + x = 7.794228634 Solving 5.5 + x = 7.794228634 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 = 7.794228634 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.794228634 + -5.5 x = 7.794228634 + -5.5 Combine like terms: 7.794228634 + -5.5 = 2.294228634 x = 2.294228634 Simplifying x = 2.294228634Subproblem 2
x + 5.5 = -7.794228634 Simplifying x + 5.5 = -7.794228634 Reorder the terms: 5.5 + x = -7.794228634 Solving 5.5 + x = -7.794228634 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 = -7.794228634 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.794228634 + -5.5 x = -7.794228634 + -5.5 Combine like terms: -7.794228634 + -5.5 = -13.294228634 x = -13.294228634 Simplifying x = -13.294228634Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.294228634, -13.294228634}Solution
x = {2.294228634, -13.294228634}
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