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Simplifying x2 + 16x + 19 = 0 Reorder the terms: 19 + 16x + x2 = 0 Solving 19 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 16x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 16x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 16x + x2 = 0 + -19 16x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 16x + x2 = -19 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 = -19 + 64 Reorder the terms: 64 + 16x + x2 = -19 + 64 Combine like terms: -19 + 64 = 45 64 + 16x + x2 = 45 Factor a perfect square on the left side: (x + 8)(x + 8) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 8) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 8 = 6.708203933 Simplifying x + 8 = 6.708203933 Reorder the terms: 8 + x = 6.708203933 Solving 8 + x = 6.708203933 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 = 6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.708203933 + -8 x = 6.708203933 + -8 Combine like terms: 6.708203933 + -8 = -1.291796067 x = -1.291796067 Simplifying x = -1.291796067Subproblem 2
x + 8 = -6.708203933 Simplifying x + 8 = -6.708203933 Reorder the terms: 8 + x = -6.708203933 Solving 8 + x = -6.708203933 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 = -6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.708203933 + -8 x = -6.708203933 + -8 Combine like terms: -6.708203933 + -8 = -14.708203933 x = -14.708203933 Simplifying x = -14.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.291796067, -14.708203933}
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