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Simplifying x2 + 16x + 43 = 0 Reorder the terms: 43 + 16x + x2 = 0 Solving 43 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 16x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 16x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 16x + x2 = 0 + -43 16x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 16x + x2 = -43 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 = -43 + 64 Reorder the terms: 64 + 16x + x2 = -43 + 64 Combine like terms: -43 + 64 = 21 64 + 16x + x2 = 21 Factor a perfect square on the left side: (x + 8)(x + 8) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 8) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 8 = 4.582575695 Simplifying x + 8 = 4.582575695 Reorder the terms: 8 + x = 4.582575695 Solving 8 + x = 4.582575695 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 = 4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.582575695 + -8 x = 4.582575695 + -8 Combine like terms: 4.582575695 + -8 = -3.417424305 x = -3.417424305 Simplifying x = -3.417424305Subproblem 2
x + 8 = -4.582575695 Simplifying x + 8 = -4.582575695 Reorder the terms: 8 + x = -4.582575695 Solving 8 + x = -4.582575695 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 = -4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.582575695 + -8 x = -4.582575695 + -8 Combine like terms: -4.582575695 + -8 = -12.582575695 x = -12.582575695 Simplifying x = -12.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.417424305, -12.582575695}
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