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Simplifying 2x2 + 22x + 24 = 0 Reorder the terms: 24 + 22x + 2x2 = 0 Solving 24 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 11x + x2)' equal to zero and attempt to solve: Simplifying 12 + 11x + x2 = 0 Solving 12 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 11x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 11x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11x + x2 = 0 + -12 11x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 11x + x2 = -12 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 = -12 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + 11x + x2 = 18.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 5.5 = 4.272001873 Simplifying x + 5.5 = 4.272001873 Reorder the terms: 5.5 + x = 4.272001873 Solving 5.5 + x = 4.272001873 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 = 4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.272001873 + -5.5 x = 4.272001873 + -5.5 Combine like terms: 4.272001873 + -5.5 = -1.227998127 x = -1.227998127 Simplifying x = -1.227998127Subproblem 2
x + 5.5 = -4.272001873 Simplifying x + 5.5 = -4.272001873 Reorder the terms: 5.5 + x = -4.272001873 Solving 5.5 + x = -4.272001873 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 = -4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.272001873 + -5.5 x = -4.272001873 + -5.5 Combine like terms: -4.272001873 + -5.5 = -9.772001873 x = -9.772001873 Simplifying x = -9.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.227998127, -9.772001873}Solution
x = {-1.227998127, -9.772001873}
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