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Simplifying 0 = X2 + 12X + -3 Reorder the terms: 0 = -3 + 12X + X2 Solving 0 = -3 + 12X + X2 Solving for variable 'X'. Combine like terms: 0 + 3 = 3 3 + -12X + -1X2 = -3 + 12X + X2 + 3 + -12X + -1X2 Reorder the terms: 3 + -12X + -1X2 = -3 + 3 + 12X + -12X + X2 + -1X2 Combine like terms: -3 + 3 = 0 3 + -12X + -1X2 = 0 + 12X + -12X + X2 + -1X2 3 + -12X + -1X2 = 12X + -12X + X2 + -1X2 Combine like terms: 12X + -12X = 0 3 + -12X + -1X2 = 0 + X2 + -1X2 3 + -12X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 3 + -12X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 12X + X2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 12X + 3 + X2 = 0 + 3 Reorder the terms: -3 + 3 + 12X + X2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 12X + X2 = 0 + 3 12X + X2 = 0 + 3 Combine like terms: 0 + 3 = 3 12X + X2 = 3 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 = 3 + 36 Reorder the terms: 36 + 12X + X2 = 3 + 36 Combine like terms: 3 + 36 = 39 36 + 12X + X2 = 39 Factor a perfect square on the left side: (X + 6)(X + 6) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (X + 6) equal to 6.244997998 and -6.244997998.Subproblem 1
X + 6 = 6.244997998 Simplifying X + 6 = 6.244997998 Reorder the terms: 6 + X = 6.244997998 Solving 6 + X = 6.244997998 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 = 6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + X = 6.244997998 + -6 X = 6.244997998 + -6 Combine like terms: 6.244997998 + -6 = 0.244997998 X = 0.244997998 Simplifying X = 0.244997998Subproblem 2
X + 6 = -6.244997998 Simplifying X + 6 = -6.244997998 Reorder the terms: 6 + X = -6.244997998 Solving 6 + X = -6.244997998 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 = -6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + X = -6.244997998 + -6 X = -6.244997998 + -6 Combine like terms: -6.244997998 + -6 = -12.244997998 X = -12.244997998 Simplifying X = -12.244997998Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.244997998, -12.244997998}
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