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Simplifying x2 + 16x = -44 Reorder the terms: 16x + x2 = -44 Solving 16x + x2 = -44 Solving for variable 'x'. Reorder the terms: 44 + 16x + x2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 16x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + 16x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 16x + x2 = 0 + -44 16x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 16x + x2 = -44 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 = -44 + 64 Reorder the terms: 64 + 16x + x2 = -44 + 64 Combine like terms: -44 + 64 = 20 64 + 16x + x2 = 20 Factor a perfect square on the left side: (x + 8)(x + 8) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 8) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 8 = 4.472135955 Simplifying x + 8 = 4.472135955 Reorder the terms: 8 + x = 4.472135955 Solving 8 + x = 4.472135955 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 = 4.472135955 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.472135955 + -8 x = 4.472135955 + -8 Combine like terms: 4.472135955 + -8 = -3.527864045 x = -3.527864045 Simplifying x = -3.527864045Subproblem 2
x + 8 = -4.472135955 Simplifying x + 8 = -4.472135955 Reorder the terms: 8 + x = -4.472135955 Solving 8 + x = -4.472135955 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 = -4.472135955 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.472135955 + -8 x = -4.472135955 + -8 Combine like terms: -4.472135955 + -8 = -12.472135955 x = -12.472135955 Simplifying x = -12.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.527864045, -12.472135955}
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