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Simplifying x2 + 8x = 3850 Reorder the terms: 8x + x2 = 3850 Solving 8x + x2 = 3850 Solving for variable 'x'. Reorder the terms: -3850 + 8x + x2 = 3850 + -3850 Combine like terms: 3850 + -3850 = 0 -3850 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3850' to each side of the equation. -3850 + 8x + 3850 + x2 = 0 + 3850 Reorder the terms: -3850 + 3850 + 8x + x2 = 0 + 3850 Combine like terms: -3850 + 3850 = 0 0 + 8x + x2 = 0 + 3850 8x + x2 = 0 + 3850 Combine like terms: 0 + 3850 = 3850 8x + x2 = 3850 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 3850 + 16 Reorder the terms: 16 + 8x + x2 = 3850 + 16 Combine like terms: 3850 + 16 = 3866 16 + 8x + x2 = 3866 Factor a perfect square on the left side: (x + 4)(x + 4) = 3866 Calculate the square root of the right side: 62.177166227 Break this problem into two subproblems by setting (x + 4) equal to 62.177166227 and -62.177166227.Subproblem 1
x + 4 = 62.177166227 Simplifying x + 4 = 62.177166227 Reorder the terms: 4 + x = 62.177166227 Solving 4 + x = 62.177166227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 62.177166227 + -4 Combine like terms: 4 + -4 = 0 0 + x = 62.177166227 + -4 x = 62.177166227 + -4 Combine like terms: 62.177166227 + -4 = 58.177166227 x = 58.177166227 Simplifying x = 58.177166227Subproblem 2
x + 4 = -62.177166227 Simplifying x + 4 = -62.177166227 Reorder the terms: 4 + x = -62.177166227 Solving 4 + x = -62.177166227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -62.177166227 + -4 Combine like terms: 4 + -4 = 0 0 + x = -62.177166227 + -4 x = -62.177166227 + -4 Combine like terms: -62.177166227 + -4 = -66.177166227 x = -66.177166227 Simplifying x = -66.177166227Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.177166227, -66.177166227}
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