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Simplifying x2 + 16x = 261 Reorder the terms: 16x + x2 = 261 Solving 16x + x2 = 261 Solving for variable 'x'. Reorder the terms: -261 + 16x + x2 = 261 + -261 Combine like terms: 261 + -261 = 0 -261 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '261' to each side of the equation. -261 + 16x + 261 + x2 = 0 + 261 Reorder the terms: -261 + 261 + 16x + x2 = 0 + 261 Combine like terms: -261 + 261 = 0 0 + 16x + x2 = 0 + 261 16x + x2 = 0 + 261 Combine like terms: 0 + 261 = 261 16x + x2 = 261 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 = 261 + 64 Reorder the terms: 64 + 16x + x2 = 261 + 64 Combine like terms: 261 + 64 = 325 64 + 16x + x2 = 325 Factor a perfect square on the left side: (x + 8)(x + 8) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + 8) equal to 18.027756377 and -18.027756377.Subproblem 1
x + 8 = 18.027756377 Simplifying x + 8 = 18.027756377 Reorder the terms: 8 + x = 18.027756377 Solving 8 + x = 18.027756377 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 = 18.027756377 + -8 Combine like terms: 8 + -8 = 0 0 + x = 18.027756377 + -8 x = 18.027756377 + -8 Combine like terms: 18.027756377 + -8 = 10.027756377 x = 10.027756377 Simplifying x = 10.027756377Subproblem 2
x + 8 = -18.027756377 Simplifying x + 8 = -18.027756377 Reorder the terms: 8 + x = -18.027756377 Solving 8 + x = -18.027756377 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 = -18.027756377 + -8 Combine like terms: 8 + -8 = 0 0 + x = -18.027756377 + -8 x = -18.027756377 + -8 Combine like terms: -18.027756377 + -8 = -26.027756377 x = -26.027756377 Simplifying x = -26.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.027756377, -26.027756377}
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