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Simplifying 212 = x(x + 16) Reorder the terms: 212 = x(16 + x) 212 = (16 * x + x * x) 212 = (16x + x2) Solving 212 = 16x + x2 Solving for variable 'x'. Reorder the terms: 212 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 212 + -16x + -1x2 = 0 + x2 + -1x2 212 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 212 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -212 + 16x + x2 = 0 Move the constant term to the right: Add '212' to each side of the equation. -212 + 16x + 212 + x2 = 0 + 212 Reorder the terms: -212 + 212 + 16x + x2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + 16x + x2 = 0 + 212 16x + x2 = 0 + 212 Combine like terms: 0 + 212 = 212 16x + x2 = 212 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 = 212 + 64 Reorder the terms: 64 + 16x + x2 = 212 + 64 Combine like terms: 212 + 64 = 276 64 + 16x + x2 = 276 Factor a perfect square on the left side: (x + 8)(x + 8) = 276 Calculate the square root of the right side: 16.613247726 Break this problem into two subproblems by setting (x + 8) equal to 16.613247726 and -16.613247726.Subproblem 1
x + 8 = 16.613247726 Simplifying x + 8 = 16.613247726 Reorder the terms: 8 + x = 16.613247726 Solving 8 + x = 16.613247726 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 = 16.613247726 + -8 Combine like terms: 8 + -8 = 0 0 + x = 16.613247726 + -8 x = 16.613247726 + -8 Combine like terms: 16.613247726 + -8 = 8.613247726 x = 8.613247726 Simplifying x = 8.613247726Subproblem 2
x + 8 = -16.613247726 Simplifying x + 8 = -16.613247726 Reorder the terms: 8 + x = -16.613247726 Solving 8 + x = -16.613247726 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 = -16.613247726 + -8 Combine like terms: 8 + -8 = 0 0 + x = -16.613247726 + -8 x = -16.613247726 + -8 Combine like terms: -16.613247726 + -8 = -24.613247726 x = -24.613247726 Simplifying x = -24.613247726Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.613247726, -24.613247726}
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