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Simplifying 12x = 3 + -1x2 Solving 12x = 3 + -1x2 Solving for variable 'x'. Reorder the terms: -3 + 12x + x2 = 3 + -1x2 + -3 + x2 Reorder the terms: -3 + 12x + x2 = 3 + -3 + -1x2 + x2 Combine like terms: 3 + -3 = 0 -3 + 12x + x2 = 0 + -1x2 + x2 -3 + 12x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3 + 12x + x2 = 0 Begin completing the square. 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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