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Simplifying x2 + 16x + -388 = 0 Reorder the terms: -388 + 16x + x2 = 0 Solving -388 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '388' to each side of the equation. -388 + 16x + 388 + x2 = 0 + 388 Reorder the terms: -388 + 388 + 16x + x2 = 0 + 388 Combine like terms: -388 + 388 = 0 0 + 16x + x2 = 0 + 388 16x + x2 = 0 + 388 Combine like terms: 0 + 388 = 388 16x + x2 = 388 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 = 388 + 64 Reorder the terms: 64 + 16x + x2 = 388 + 64 Combine like terms: 388 + 64 = 452 64 + 16x + x2 = 452 Factor a perfect square on the left side: (x + 8)(x + 8) = 452 Calculate the square root of the right side: 21.260291625 Break this problem into two subproblems by setting (x + 8) equal to 21.260291625 and -21.260291625.Subproblem 1
x + 8 = 21.260291625 Simplifying x + 8 = 21.260291625 Reorder the terms: 8 + x = 21.260291625 Solving 8 + x = 21.260291625 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 = 21.260291625 + -8 Combine like terms: 8 + -8 = 0 0 + x = 21.260291625 + -8 x = 21.260291625 + -8 Combine like terms: 21.260291625 + -8 = 13.260291625 x = 13.260291625 Simplifying x = 13.260291625Subproblem 2
x + 8 = -21.260291625 Simplifying x + 8 = -21.260291625 Reorder the terms: 8 + x = -21.260291625 Solving 8 + x = -21.260291625 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 = -21.260291625 + -8 Combine like terms: 8 + -8 = 0 0 + x = -21.260291625 + -8 x = -21.260291625 + -8 Combine like terms: -21.260291625 + -8 = -29.260291625 x = -29.260291625 Simplifying x = -29.260291625Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.260291625, -29.260291625}
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