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Simplifying x2 + -8x + -16 = 169 Reorder the terms: -16 + -8x + x2 = 169 Solving -16 + -8x + x2 = 169 Solving for variable 'x'. Reorder the terms: -16 + -169 + -8x + x2 = 169 + -169 Combine like terms: -16 + -169 = -185 -185 + -8x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -185 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + -8x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + -8x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + -8x + x2 = 0 + 185 -8x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 -8x + x2 = 185 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 = 185 + 16 Reorder the terms: 16 + -8x + x2 = 185 + 16 Combine like terms: 185 + 16 = 201 16 + -8x + x2 = 201 Factor a perfect square on the left side: (x + -4)(x + -4) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + -4) equal to 14.177446879 and -14.177446879.Subproblem 1
x + -4 = 14.177446879 Simplifying x + -4 = 14.177446879 Reorder the terms: -4 + x = 14.177446879 Solving -4 + x = 14.177446879 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 = 14.177446879 + 4 Combine like terms: -4 + 4 = 0 0 + x = 14.177446879 + 4 x = 14.177446879 + 4 Combine like terms: 14.177446879 + 4 = 18.177446879 x = 18.177446879 Simplifying x = 18.177446879Subproblem 2
x + -4 = -14.177446879 Simplifying x + -4 = -14.177446879 Reorder the terms: -4 + x = -14.177446879 Solving -4 + x = -14.177446879 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 = -14.177446879 + 4 Combine like terms: -4 + 4 = 0 0 + x = -14.177446879 + 4 x = -14.177446879 + 4 Combine like terms: -14.177446879 + 4 = -10.177446879 x = -10.177446879 Simplifying x = -10.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.177446879, -10.177446879}
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