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Simplifying x2 + 12x = 42 Reorder the terms: 12x + x2 = 42 Solving 12x + x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 12x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 12x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 12x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 12x + x2 = 0 + 42 12x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 12x + x2 = 42 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 = 42 + 36 Reorder the terms: 36 + 12x + x2 = 42 + 36 Combine like terms: 42 + 36 = 78 36 + 12x + x2 = 78 Factor a perfect square on the left side: (x + 6)(x + 6) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 6) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 6 = 8.831760866 Simplifying x + 6 = 8.831760866 Reorder the terms: 6 + x = 8.831760866 Solving 6 + x = 8.831760866 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 = 8.831760866 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.831760866 + -6 x = 8.831760866 + -6 Combine like terms: 8.831760866 + -6 = 2.831760866 x = 2.831760866 Simplifying x = 2.831760866Subproblem 2
x + 6 = -8.831760866 Simplifying x + 6 = -8.831760866 Reorder the terms: 6 + x = -8.831760866 Solving 6 + x = -8.831760866 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 = -8.831760866 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.831760866 + -6 x = -8.831760866 + -6 Combine like terms: -8.831760866 + -6 = -14.831760866 x = -14.831760866 Simplifying x = -14.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.831760866, -14.831760866}
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