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Simplifying x2 + 8x = 201 Reorder the terms: 8x + x2 = 201 Solving 8x + x2 = 201 Solving for variable 'x'. Reorder the terms: -201 + 8x + x2 = 201 + -201 Combine like terms: 201 + -201 = 0 -201 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '201' to each side of the equation. -201 + 8x + 201 + x2 = 0 + 201 Reorder the terms: -201 + 201 + 8x + x2 = 0 + 201 Combine like terms: -201 + 201 = 0 0 + 8x + x2 = 0 + 201 8x + x2 = 0 + 201 Combine like terms: 0 + 201 = 201 8x + x2 = 201 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 = 201 + 16 Reorder the terms: 16 + 8x + x2 = 201 + 16 Combine like terms: 201 + 16 = 217 16 + 8x + x2 = 217 Factor a perfect square on the left side: (x + 4)(x + 4) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 4) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 4 = 14.730919863 Simplifying x + 4 = 14.730919863 Reorder the terms: 4 + x = 14.730919863 Solving 4 + x = 14.730919863 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 = 14.730919863 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.730919863 + -4 x = 14.730919863 + -4 Combine like terms: 14.730919863 + -4 = 10.730919863 x = 10.730919863 Simplifying x = 10.730919863Subproblem 2
x + 4 = -14.730919863 Simplifying x + 4 = -14.730919863 Reorder the terms: 4 + x = -14.730919863 Solving 4 + x = -14.730919863 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 = -14.730919863 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.730919863 + -4 x = -14.730919863 + -4 Combine like terms: -14.730919863 + -4 = -18.730919863 x = -18.730919863 Simplifying x = -18.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.730919863, -18.730919863}
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