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Simplifying 4(X2 + 12X + -164) = 0 Reorder the terms: 4(-164 + 12X + X2) = 0 (-164 * 4 + 12X * 4 + X2 * 4) = 0 (-656 + 48X + 4X2) = 0 Solving -656 + 48X + 4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(-164 + 12X + X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-164 + 12X + X2)' equal to zero and attempt to solve: Simplifying -164 + 12X + X2 = 0 Solving -164 + 12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 12X + 164 + X2 = 0 + 164 Reorder the terms: -164 + 164 + 12X + X2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 12X + X2 = 0 + 164 12X + X2 = 0 + 164 Combine like terms: 0 + 164 = 164 12X + X2 = 164 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 = 164 + 36 Reorder the terms: 36 + 12X + X2 = 164 + 36 Combine like terms: 164 + 36 = 200 36 + 12X + X2 = 200 Factor a perfect square on the left side: (X + 6)(X + 6) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (X + 6) equal to 14.142135624 and -14.142135624.Subproblem 1
X + 6 = 14.142135624 Simplifying X + 6 = 14.142135624 Reorder the terms: 6 + X = 14.142135624 Solving 6 + X = 14.142135624 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 = 14.142135624 + -6 Combine like terms: 6 + -6 = 0 0 + X = 14.142135624 + -6 X = 14.142135624 + -6 Combine like terms: 14.142135624 + -6 = 8.142135624 X = 8.142135624 Simplifying X = 8.142135624Subproblem 2
X + 6 = -14.142135624 Simplifying X + 6 = -14.142135624 Reorder the terms: 6 + X = -14.142135624 Solving 6 + X = -14.142135624 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 = -14.142135624 + -6 Combine like terms: 6 + -6 = 0 0 + X = -14.142135624 + -6 X = -14.142135624 + -6 Combine like terms: -14.142135624 + -6 = -20.142135624 X = -20.142135624 Simplifying X = -20.142135624Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.142135624, -20.142135624}Solution
X = {8.142135624, -20.142135624}
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