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Simplifying x2 + 16x + 54 = 0 Reorder the terms: 54 + 16x + x2 = 0 Solving 54 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 16x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + 16x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 16x + x2 = 0 + -54 16x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 16x + x2 = -54 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 = -54 + 64 Reorder the terms: 64 + 16x + x2 = -54 + 64 Combine like terms: -54 + 64 = 10 64 + 16x + x2 = 10 Factor a perfect square on the left side: (x + 8)(x + 8) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 8) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 8 = 3.16227766 Simplifying x + 8 = 3.16227766 Reorder the terms: 8 + x = 3.16227766 Solving 8 + x = 3.16227766 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 = 3.16227766 + -8 Combine like terms: 8 + -8 = 0 0 + x = 3.16227766 + -8 x = 3.16227766 + -8 Combine like terms: 3.16227766 + -8 = -4.83772234 x = -4.83772234 Simplifying x = -4.83772234Subproblem 2
x + 8 = -3.16227766 Simplifying x + 8 = -3.16227766 Reorder the terms: 8 + x = -3.16227766 Solving 8 + x = -3.16227766 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 = -3.16227766 + -8 Combine like terms: 8 + -8 = 0 0 + x = -3.16227766 + -8 x = -3.16227766 + -8 Combine like terms: -3.16227766 + -8 = -11.16227766 x = -11.16227766 Simplifying x = -11.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.83772234, -11.16227766}
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