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Simplifying 112 = x2 + 16x Reorder the terms: 112 = 16x + x2 Solving 112 = 16x + x2 Solving for variable 'x'. Reorder the terms: 112 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 112 + -16x + -1x2 = 0 + x2 + -1x2 112 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 112 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -112 + 16x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + 16x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 16x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 16x + x2 = 0 + 112 16x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 16x + x2 = 112 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 = 112 + 64 Reorder the terms: 64 + 16x + x2 = 112 + 64 Combine like terms: 112 + 64 = 176 64 + 16x + x2 = 176 Factor a perfect square on the left side: (x + 8)(x + 8) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + 8) equal to 13.266499161 and -13.266499161.Subproblem 1
x + 8 = 13.266499161 Simplifying x + 8 = 13.266499161 Reorder the terms: 8 + x = 13.266499161 Solving 8 + x = 13.266499161 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 = 13.266499161 + -8 Combine like terms: 8 + -8 = 0 0 + x = 13.266499161 + -8 x = 13.266499161 + -8 Combine like terms: 13.266499161 + -8 = 5.266499161 x = 5.266499161 Simplifying x = 5.266499161Subproblem 2
x + 8 = -13.266499161 Simplifying x + 8 = -13.266499161 Reorder the terms: 8 + x = -13.266499161 Solving 8 + x = -13.266499161 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 = -13.266499161 + -8 Combine like terms: 8 + -8 = 0 0 + x = -13.266499161 + -8 x = -13.266499161 + -8 Combine like terms: -13.266499161 + -8 = -21.266499161 x = -21.266499161 Simplifying x = -21.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.266499161, -21.266499161}
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