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Simplifying x2 + 12x = -4 Reorder the terms: 12x + x2 = -4 Solving 12x + x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 12x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 12x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 12x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 12x + x2 = 0 + -4 12x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 12x + x2 = -4 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 = -4 + 36 Reorder the terms: 36 + 12x + x2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + 12x + x2 = 32 Factor a perfect square on the left side: (x + 6)(x + 6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 6) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 6 = 5.656854249 Simplifying x + 6 = 5.656854249 Reorder the terms: 6 + x = 5.656854249 Solving 6 + x = 5.656854249 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 = 5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.656854249 + -6 x = 5.656854249 + -6 Combine like terms: 5.656854249 + -6 = -0.343145751 x = -0.343145751 Simplifying x = -0.343145751Subproblem 2
x + 6 = -5.656854249 Simplifying x + 6 = -5.656854249 Reorder the terms: 6 + x = -5.656854249 Solving 6 + x = -5.656854249 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 = -5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.656854249 + -6 x = -5.656854249 + -6 Combine like terms: -5.656854249 + -6 = -11.656854249 x = -11.656854249 Simplifying x = -11.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.343145751, -11.656854249}
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