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Simplifying x2 + 12x = 16 Reorder the terms: 12x + x2 = 16 Solving 12x + x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 12x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 12x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 12x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 12x + x2 = 0 + 16 12x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 12x + x2 = 16 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 = 16 + 36 Reorder the terms: 36 + 12x + x2 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + 12x + x2 = 52 Factor a perfect square on the left side: (x + 6)(x + 6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 6) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 6 = 7.211102551 Simplifying x + 6 = 7.211102551 Reorder the terms: 6 + x = 7.211102551 Solving 6 + x = 7.211102551 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 = 7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.211102551 + -6 x = 7.211102551 + -6 Combine like terms: 7.211102551 + -6 = 1.211102551 x = 1.211102551 Simplifying x = 1.211102551Subproblem 2
x + 6 = -7.211102551 Simplifying x + 6 = -7.211102551 Reorder the terms: 6 + x = -7.211102551 Solving 6 + x = -7.211102551 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 = -7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.211102551 + -6 x = -7.211102551 + -6 Combine like terms: -7.211102551 + -6 = -13.211102551 x = -13.211102551 Simplifying x = -13.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.211102551, -13.211102551}
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