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Simplifying 2x2 + -20x + -44 = 0 Reorder the terms: -44 + -20x + 2x2 = 0 Solving -44 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + -10x + x2)' equal to zero and attempt to solve: Simplifying -22 + -10x + x2 = 0 Solving -22 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -10x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -10x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -10x + x2 = 0 + 22 -10x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -10x + x2 = 22 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 22 + 25 Reorder the terms: 25 + -10x + x2 = 22 + 25 Combine like terms: 22 + 25 = 47 25 + -10x + x2 = 47 Factor a perfect square on the left side: (x + -5)(x + -5) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -5) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -5 = 6.8556546 Simplifying x + -5 = 6.8556546 Reorder the terms: -5 + x = 6.8556546 Solving -5 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.8556546 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.8556546 + 5 x = 6.8556546 + 5 Combine like terms: 6.8556546 + 5 = 11.8556546 x = 11.8556546 Simplifying x = 11.8556546Subproblem 2
x + -5 = -6.8556546 Simplifying x + -5 = -6.8556546 Reorder the terms: -5 + x = -6.8556546 Solving -5 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.8556546 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.8556546 + 5 x = -6.8556546 + 5 Combine like terms: -6.8556546 + 5 = -1.8556546 x = -1.8556546 Simplifying x = -1.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.8556546, -1.8556546}Solution
x = {11.8556546, -1.8556546}
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