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Simplifying (12X + 24)(2X + 8) = 6 Reorder the terms: (24 + 12X)(2X + 8) = 6 Reorder the terms: (24 + 12X)(8 + 2X) = 6 Multiply (24 + 12X) * (8 + 2X) (24(8 + 2X) + 12X * (8 + 2X)) = 6 ((8 * 24 + 2X * 24) + 12X * (8 + 2X)) = 6 ((192 + 48X) + 12X * (8 + 2X)) = 6 (192 + 48X + (8 * 12X + 2X * 12X)) = 6 (192 + 48X + (96X + 24X2)) = 6 Combine like terms: 48X + 96X = 144X (192 + 144X + 24X2) = 6 Solving 192 + 144X + 24X2 = 6 Solving for variable 'X'. Reorder the terms: 192 + -6 + 144X + 24X2 = 6 + -6 Combine like terms: 192 + -6 = 186 186 + 144X + 24X2 = 6 + -6 Combine like terms: 6 + -6 = 0 186 + 144X + 24X2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(31 + 24X + 4X2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(31 + 24X + 4X2)' equal to zero and attempt to solve: Simplifying 31 + 24X + 4X2 = 0 Solving 31 + 24X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.75 + 6X + X2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + 6X + -7.75 + X2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + 6X + X2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + 6X + X2 = 0 + -7.75 6X + X2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 6X + X2 = -7.75 The X term is 6X. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6X + 9 + X2 = -7.75 + 9 Reorder the terms: 9 + 6X + X2 = -7.75 + 9 Combine like terms: -7.75 + 9 = 1.25 9 + 6X + X2 = 1.25 Factor a perfect square on the left side: (X + 3)(X + 3) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (X + 3) equal to 1.118033989 and -1.118033989.Subproblem 1
X + 3 = 1.118033989 Simplifying X + 3 = 1.118033989 Reorder the terms: 3 + X = 1.118033989 Solving 3 + X = 1.118033989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 1.118033989 + -3 Combine like terms: 3 + -3 = 0 0 + X = 1.118033989 + -3 X = 1.118033989 + -3 Combine like terms: 1.118033989 + -3 = -1.881966011 X = -1.881966011 Simplifying X = -1.881966011Subproblem 2
X + 3 = -1.118033989 Simplifying X + 3 = -1.118033989 Reorder the terms: 3 + X = -1.118033989 Solving 3 + X = -1.118033989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -1.118033989 + -3 Combine like terms: 3 + -3 = 0 0 + X = -1.118033989 + -3 X = -1.118033989 + -3 Combine like terms: -1.118033989 + -3 = -4.118033989 X = -4.118033989 Simplifying X = -4.118033989Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.881966011, -4.118033989}Solution
X = {-1.881966011, -4.118033989}
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