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Simplifying x2 + 12x + -6 = 4 Reorder the terms: -6 + 12x + x2 = 4 Solving -6 + 12x + x2 = 4 Solving for variable 'x'. Reorder the terms: -6 + -4 + 12x + x2 = 4 + -4 Combine like terms: -6 + -4 = -10 -10 + 12x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -10 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 12x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 12x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 12x + x2 = 0 + 10 12x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 12x + x2 = 10 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 = 10 + 36 Reorder the terms: 36 + 12x + x2 = 10 + 36 Combine like terms: 10 + 36 = 46 36 + 12x + x2 = 46 Factor a perfect square on the left side: (x + 6)(x + 6) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 6) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 6 = 6.782329983 Simplifying x + 6 = 6.782329983 Reorder the terms: 6 + x = 6.782329983 Solving 6 + x = 6.782329983 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 = 6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.782329983 + -6 x = 6.782329983 + -6 Combine like terms: 6.782329983 + -6 = 0.782329983 x = 0.782329983 Simplifying x = 0.782329983Subproblem 2
x + 6 = -6.782329983 Simplifying x + 6 = -6.782329983 Reorder the terms: 6 + x = -6.782329983 Solving 6 + x = -6.782329983 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 = -6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.782329983 + -6 x = -6.782329983 + -6 Combine like terms: -6.782329983 + -6 = -12.782329983 x = -12.782329983 Simplifying x = -12.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.782329983, -12.782329983}
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