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Simplifying 12X2 + 72X + -78 = 0 Reorder the terms: -78 + 72X + 12X2 = 0 Solving -78 + 72X + 12X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '6'. 6(-13 + 12X + 2X2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-13 + 12X + 2X2)' equal to zero and attempt to solve: Simplifying -13 + 12X + 2X2 = 0 Solving -13 + 12X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 6X + X2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 6X + 6.5 + X2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 6X + X2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 6X + X2 = 0 + 6.5 6X + X2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 6X + X2 = 6.5 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 = 6.5 + 9 Reorder the terms: 9 + 6X + X2 = 6.5 + 9 Combine like terms: 6.5 + 9 = 15.5 9 + 6X + X2 = 15.5 Factor a perfect square on the left side: (X + 3)(X + 3) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (X + 3) equal to 3.937003937 and -3.937003937.Subproblem 1
X + 3 = 3.937003937 Simplifying X + 3 = 3.937003937 Reorder the terms: 3 + X = 3.937003937 Solving 3 + X = 3.937003937 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 = 3.937003937 + -3 Combine like terms: 3 + -3 = 0 0 + X = 3.937003937 + -3 X = 3.937003937 + -3 Combine like terms: 3.937003937 + -3 = 0.937003937 X = 0.937003937 Simplifying X = 0.937003937Subproblem 2
X + 3 = -3.937003937 Simplifying X + 3 = -3.937003937 Reorder the terms: 3 + X = -3.937003937 Solving 3 + X = -3.937003937 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 = -3.937003937 + -3 Combine like terms: 3 + -3 = 0 0 + X = -3.937003937 + -3 X = -3.937003937 + -3 Combine like terms: -3.937003937 + -3 = -6.937003937 X = -6.937003937 Simplifying X = -6.937003937Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.937003937, -6.937003937}Solution
X = {0.937003937, -6.937003937}
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