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Simplifying x2 + 12x + 3 = 2 Reorder the terms: 3 + 12x + x2 = 2 Solving 3 + 12x + x2 = 2 Solving for variable 'x'. Reorder the terms: 3 + -2 + 12x + x2 = 2 + -2 Combine like terms: 3 + -2 = 1 1 + 12x + x2 = 2 + -2 Combine like terms: 2 + -2 = 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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