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Simplifying 4X2 + -48X + -92 = 0 Reorder the terms: -92 + -48X + 4X2 = 0 Solving -92 + -48X + 4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + -12X + X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + -12X + X2)' equal to zero and attempt to solve: Simplifying -23 + -12X + X2 = 0 Solving -23 + -12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -12X + 23 + X2 = 0 + 23 Reorder the terms: -23 + 23 + -12X + X2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -12X + X2 = 0 + 23 -12X + X2 = 0 + 23 Combine like terms: 0 + 23 = 23 -12X + X2 = 23 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = 23 + 36 Reorder the terms: 36 + -12X + X2 = 23 + 36 Combine like terms: 23 + 36 = 59 36 + -12X + X2 = 59 Factor a perfect square on the left side: (X + -6)(X + -6) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (X + -6) equal to 7.681145748 and -7.681145748.Subproblem 1
X + -6 = 7.681145748 Simplifying X + -6 = 7.681145748 Reorder the terms: -6 + X = 7.681145748 Solving -6 + X = 7.681145748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 7.681145748 + 6 Combine like terms: -6 + 6 = 0 0 + X = 7.681145748 + 6 X = 7.681145748 + 6 Combine like terms: 7.681145748 + 6 = 13.681145748 X = 13.681145748 Simplifying X = 13.681145748Subproblem 2
X + -6 = -7.681145748 Simplifying X + -6 = -7.681145748 Reorder the terms: -6 + X = -7.681145748 Solving -6 + X = -7.681145748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -7.681145748 + 6 Combine like terms: -6 + 6 = 0 0 + X = -7.681145748 + 6 X = -7.681145748 + 6 Combine like terms: -7.681145748 + 6 = -1.681145748 X = -1.681145748 Simplifying X = -1.681145748Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.681145748, -1.681145748}Solution
X = {13.681145748, -1.681145748}
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