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Simplifying x2 + 16x = 216 Reorder the terms: 16x + x2 = 216 Solving 16x + x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + 16x + x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 16x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 16x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 16x + x2 = 0 + 216 16x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 16x + x2 = 216 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 = 216 + 64 Reorder the terms: 64 + 16x + x2 = 216 + 64 Combine like terms: 216 + 64 = 280 64 + 16x + x2 = 280 Factor a perfect square on the left side: (x + 8)(x + 8) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 8) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 8 = 16.733200531 Simplifying x + 8 = 16.733200531 Reorder the terms: 8 + x = 16.733200531 Solving 8 + x = 16.733200531 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 = 16.733200531 + -8 Combine like terms: 8 + -8 = 0 0 + x = 16.733200531 + -8 x = 16.733200531 + -8 Combine like terms: 16.733200531 + -8 = 8.733200531 x = 8.733200531 Simplifying x = 8.733200531Subproblem 2
x + 8 = -16.733200531 Simplifying x + 8 = -16.733200531 Reorder the terms: 8 + x = -16.733200531 Solving 8 + x = -16.733200531 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 = -16.733200531 + -8 Combine like terms: 8 + -8 = 0 0 + x = -16.733200531 + -8 x = -16.733200531 + -8 Combine like terms: -16.733200531 + -8 = -24.733200531 x = -24.733200531 Simplifying x = -24.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.733200531, -24.733200531}
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