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Simplifying x2 + 26x = 32 Reorder the terms: 26x + x2 = 32 Solving 26x + x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 26x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 26x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 26x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 26x + x2 = 0 + 32 26x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 26x + x2 = 32 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 32 + 169 Reorder the terms: 169 + 26x + x2 = 32 + 169 Combine like terms: 32 + 169 = 201 169 + 26x + x2 = 201 Factor a perfect square on the left side: (x + 13)(x + 13) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + 13) equal to 14.177446879 and -14.177446879.Subproblem 1
x + 13 = 14.177446879 Simplifying x + 13 = 14.177446879 Reorder the terms: 13 + x = 14.177446879 Solving 13 + x = 14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 14.177446879 + -13 Combine like terms: 13 + -13 = 0 0 + x = 14.177446879 + -13 x = 14.177446879 + -13 Combine like terms: 14.177446879 + -13 = 1.177446879 x = 1.177446879 Simplifying x = 1.177446879Subproblem 2
x + 13 = -14.177446879 Simplifying x + 13 = -14.177446879 Reorder the terms: 13 + x = -14.177446879 Solving 13 + x = -14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -14.177446879 + -13 Combine like terms: 13 + -13 = 0 0 + x = -14.177446879 + -13 x = -14.177446879 + -13 Combine like terms: -14.177446879 + -13 = -27.177446879 x = -27.177446879 Simplifying x = -27.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.177446879, -27.177446879}
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