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Simplifying x2 + 16x + 12 = 0 Reorder the terms: 12 + 16x + x2 = 0 Solving 12 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 16x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 16x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 16x + x2 = 0 + -12 16x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 16x + x2 = -12 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -12 + 64 Reorder the terms: 64 + 16x + x2 = -12 + 64 Combine like terms: -12 + 64 = 52 64 + 16x + x2 = 52 Factor a perfect square on the left side: (x + 8)(x + 8) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 8) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 8 = 7.211102551 Simplifying x + 8 = 7.211102551 Reorder the terms: 8 + x = 7.211102551 Solving 8 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.211102551 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.211102551 + -8 x = 7.211102551 + -8 Combine like terms: 7.211102551 + -8 = -0.788897449 x = -0.788897449 Simplifying x = -0.788897449Subproblem 2
x + 8 = -7.211102551 Simplifying x + 8 = -7.211102551 Reorder the terms: 8 + x = -7.211102551 Solving 8 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.211102551 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.211102551 + -8 x = -7.211102551 + -8 Combine like terms: -7.211102551 + -8 = -15.211102551 x = -15.211102551 Simplifying x = -15.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.788897449, -15.211102551}
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