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Simplifying x2 + 16x + -48 = 6 Reorder the terms: -48 + 16x + x2 = 6 Solving -48 + 16x + x2 = 6 Solving for variable 'x'. Reorder the terms: -48 + -6 + 16x + x2 = 6 + -6 Combine like terms: -48 + -6 = -54 -54 + 16x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -54 + 16x + x2 = 0 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 = 118 64 + 16x + x2 = 118 Factor a perfect square on the left side: (x + 8)(x + 8) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (x + 8) equal to 10.862780491 and -10.862780491.Subproblem 1
x + 8 = 10.862780491 Simplifying x + 8 = 10.862780491 Reorder the terms: 8 + x = 10.862780491 Solving 8 + x = 10.862780491 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 = 10.862780491 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.862780491 + -8 x = 10.862780491 + -8 Combine like terms: 10.862780491 + -8 = 2.862780491 x = 2.862780491 Simplifying x = 2.862780491Subproblem 2
x + 8 = -10.862780491 Simplifying x + 8 = -10.862780491 Reorder the terms: 8 + x = -10.862780491 Solving 8 + x = -10.862780491 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 = -10.862780491 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.862780491 + -8 x = -10.862780491 + -8 Combine like terms: -10.862780491 + -8 = -18.862780491 x = -18.862780491 Simplifying x = -18.862780491Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.862780491, -18.862780491}
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