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Simplifying 4x2 + -44x + -24 = 0 Reorder the terms: -24 + -44x + 4x2 = 0 Solving -24 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -11x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -11x + x2)' equal to zero and attempt to solve: Simplifying -6 + -11x + x2 = 0 Solving -6 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -11x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -11x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -11x + x2 = 0 + 6 -11x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -11x + x2 = 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 = 6 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + -11x + x2 = 36.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -5.5 = 6.020797289 Simplifying x + -5.5 = 6.020797289 Reorder the terms: -5.5 + x = 6.020797289 Solving -5.5 + x = 6.020797289 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 = 6.020797289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.020797289 + 5.5 x = 6.020797289 + 5.5 Combine like terms: 6.020797289 + 5.5 = 11.520797289 x = 11.520797289 Simplifying x = 11.520797289Subproblem 2
x + -5.5 = -6.020797289 Simplifying x + -5.5 = -6.020797289 Reorder the terms: -5.5 + x = -6.020797289 Solving -5.5 + x = -6.020797289 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 = -6.020797289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.020797289 + 5.5 x = -6.020797289 + 5.5 Combine like terms: -6.020797289 + 5.5 = -0.520797289 x = -0.520797289 Simplifying x = -0.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.520797289, -0.520797289}Solution
x = {11.520797289, -0.520797289}
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