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Simplifying X2 + 12X = -1 Reorder the terms: 12X + X2 = -1 Solving 12X + X2 = -1 Solving for variable 'X'. Reorder the terms: 1 + 12X + X2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 12X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + 12X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 12X + X2 = 0 + -1 12X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 12X + X2 = -1 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 = -1 + 36 Reorder the terms: 36 + 12X + X2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + 12X + X2 = 35 Factor a perfect square on the left side: (X + 6)(X + 6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (X + 6) equal to 5.916079783 and -5.916079783.Subproblem 1
X + 6 = 5.916079783 Simplifying X + 6 = 5.916079783 Reorder the terms: 6 + X = 5.916079783 Solving 6 + X = 5.916079783 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 = 5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + X = 5.916079783 + -6 X = 5.916079783 + -6 Combine like terms: 5.916079783 + -6 = -0.083920217 X = -0.083920217 Simplifying X = -0.083920217Subproblem 2
X + 6 = -5.916079783 Simplifying X + 6 = -5.916079783 Reorder the terms: 6 + X = -5.916079783 Solving 6 + X = -5.916079783 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 = -5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + X = -5.916079783 + -6 X = -5.916079783 + -6 Combine like terms: -5.916079783 + -6 = -11.916079783 X = -11.916079783 Simplifying X = -11.916079783Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.083920217, -11.916079783}
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