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Simplifying 4x2 + -44x + 116 = 0 Reorder the terms: 116 + -44x + 4x2 = 0 Solving 116 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -11x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -11x + x2)' equal to zero and attempt to solve: Simplifying 29 + -11x + x2 = 0 Solving 29 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -11x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -11x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -11x + x2 = 0 + -29 -11x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -11x + x2 = -29 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 = -29 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29 + 30.25 Combine like terms: -29 + 30.25 = 1.25 30.25 + -11x + x2 = 1.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -5.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -5.5 = 1.118033989 Simplifying x + -5.5 = 1.118033989 Reorder the terms: -5.5 + x = 1.118033989 Solving -5.5 + x = 1.118033989 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 = 1.118033989 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 1.118033989 + 5.5 x = 1.118033989 + 5.5 Combine like terms: 1.118033989 + 5.5 = 6.618033989 x = 6.618033989 Simplifying x = 6.618033989Subproblem 2
x + -5.5 = -1.118033989 Simplifying x + -5.5 = -1.118033989 Reorder the terms: -5.5 + x = -1.118033989 Solving -5.5 + x = -1.118033989 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 = -1.118033989 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -1.118033989 + 5.5 x = -1.118033989 + 5.5 Combine like terms: -1.118033989 + 5.5 = 4.381966011 x = 4.381966011 Simplifying x = 4.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.618033989, 4.381966011}Solution
x = {6.618033989, 4.381966011}
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