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Simplifying x2 + 16x = 305 Reorder the terms: 16x + x2 = 305 Solving 16x + x2 = 305 Solving for variable 'x'. Reorder the terms: -305 + 16x + x2 = 305 + -305 Combine like terms: 305 + -305 = 0 -305 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '305' to each side of the equation. -305 + 16x + 305 + x2 = 0 + 305 Reorder the terms: -305 + 305 + 16x + x2 = 0 + 305 Combine like terms: -305 + 305 = 0 0 + 16x + x2 = 0 + 305 16x + x2 = 0 + 305 Combine like terms: 0 + 305 = 305 16x + x2 = 305 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 = 305 + 64 Reorder the terms: 64 + 16x + x2 = 305 + 64 Combine like terms: 305 + 64 = 369 64 + 16x + x2 = 369 Factor a perfect square on the left side: (x + 8)(x + 8) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + 8) equal to 19.209372712 and -19.209372712.Subproblem 1
x + 8 = 19.209372712 Simplifying x + 8 = 19.209372712 Reorder the terms: 8 + x = 19.209372712 Solving 8 + x = 19.209372712 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 = 19.209372712 + -8 Combine like terms: 8 + -8 = 0 0 + x = 19.209372712 + -8 x = 19.209372712 + -8 Combine like terms: 19.209372712 + -8 = 11.209372712 x = 11.209372712 Simplifying x = 11.209372712Subproblem 2
x + 8 = -19.209372712 Simplifying x + 8 = -19.209372712 Reorder the terms: 8 + x = -19.209372712 Solving 8 + x = -19.209372712 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 = -19.209372712 + -8 Combine like terms: 8 + -8 = 0 0 + x = -19.209372712 + -8 x = -19.209372712 + -8 Combine like terms: -19.209372712 + -8 = -27.209372712 x = -27.209372712 Simplifying x = -27.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.209372712, -27.209372712}
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