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Simplifying 6X2 + -48X + 92 = 0 Reorder the terms: 92 + -48X + 6X2 = 0 Solving 92 + -48X + 6X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(46 + -24X + 3X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(46 + -24X + 3X2)' equal to zero and attempt to solve: Simplifying 46 + -24X + 3X2 = 0 Solving 46 + -24X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.33333333 + -8X + X2 = 0 Move the constant term to the right: Add '-15.33333333' to each side of the equation. 15.33333333 + -8X + -15.33333333 + X2 = 0 + -15.33333333 Reorder the terms: 15.33333333 + -15.33333333 + -8X + X2 = 0 + -15.33333333 Combine like terms: 15.33333333 + -15.33333333 = 0.00000000 0.00000000 + -8X + X2 = 0 + -15.33333333 -8X + X2 = 0 + -15.33333333 Combine like terms: 0 + -15.33333333 = -15.33333333 -8X + X2 = -15.33333333 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = -15.33333333 + 16 Reorder the terms: 16 + -8X + X2 = -15.33333333 + 16 Combine like terms: -15.33333333 + 16 = 0.66666667 16 + -8X + X2 = 0.66666667 Factor a perfect square on the left side: (X + -4)(X + -4) = 0.66666667 Calculate the square root of the right side: 0.816496583 Break this problem into two subproblems by setting (X + -4) equal to 0.816496583 and -0.816496583.Subproblem 1
X + -4 = 0.816496583 Simplifying X + -4 = 0.816496583 Reorder the terms: -4 + X = 0.816496583 Solving -4 + X = 0.816496583 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 0.816496583 + 4 Combine like terms: -4 + 4 = 0 0 + X = 0.816496583 + 4 X = 0.816496583 + 4 Combine like terms: 0.816496583 + 4 = 4.816496583 X = 4.816496583 Simplifying X = 4.816496583Subproblem 2
X + -4 = -0.816496583 Simplifying X + -4 = -0.816496583 Reorder the terms: -4 + X = -0.816496583 Solving -4 + X = -0.816496583 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -0.816496583 + 4 Combine like terms: -4 + 4 = 0 0 + X = -0.816496583 + 4 X = -0.816496583 + 4 Combine like terms: -0.816496583 + 4 = 3.183503417 X = 3.183503417 Simplifying X = 3.183503417Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.816496583, 3.183503417}Solution
X = {4.816496583, 3.183503417}
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