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Simplifying x2 + 16x + 47 = 0 Reorder the terms: 47 + 16x + x2 = 0 Solving 47 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 16x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 16x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 16x + x2 = 0 + -47 16x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 16x + x2 = -47 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 = -47 + 64 Reorder the terms: 64 + 16x + x2 = -47 + 64 Combine like terms: -47 + 64 = 17 64 + 16x + x2 = 17 Factor a perfect square on the left side: (x + 8)(x + 8) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 8) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 8 = 4.123105626 Simplifying x + 8 = 4.123105626 Reorder the terms: 8 + x = 4.123105626 Solving 8 + x = 4.123105626 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 = 4.123105626 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.123105626 + -8 x = 4.123105626 + -8 Combine like terms: 4.123105626 + -8 = -3.876894374 x = -3.876894374 Simplifying x = -3.876894374Subproblem 2
x + 8 = -4.123105626 Simplifying x + 8 = -4.123105626 Reorder the terms: 8 + x = -4.123105626 Solving 8 + x = -4.123105626 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 = -4.123105626 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.123105626 + -8 x = -4.123105626 + -8 Combine like terms: -4.123105626 + -8 = -12.123105626 x = -12.123105626 Simplifying x = -12.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.876894374, -12.123105626}
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