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Simplifying x2 = 26x + 197 Reorder the terms: x2 = 197 + 26x Solving x2 = 197 + 26x Solving for variable 'x'. Reorder the terms: -197 + -26x + x2 = 197 + 26x + -197 + -26x Reorder the terms: -197 + -26x + x2 = 197 + -197 + 26x + -26x Combine like terms: 197 + -197 = 0 -197 + -26x + x2 = 0 + 26x + -26x -197 + -26x + x2 = 26x + -26x Combine like terms: 26x + -26x = 0 -197 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '197' to each side of the equation. -197 + -26x + 197 + x2 = 0 + 197 Reorder the terms: -197 + 197 + -26x + x2 = 0 + 197 Combine like terms: -197 + 197 = 0 0 + -26x + x2 = 0 + 197 -26x + x2 = 0 + 197 Combine like terms: 0 + 197 = 197 -26x + x2 = 197 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 = 197 + 169 Reorder the terms: 169 + -26x + x2 = 197 + 169 Combine like terms: 197 + 169 = 366 169 + -26x + x2 = 366 Factor a perfect square on the left side: (x + -13)(x + -13) = 366 Calculate the square root of the right side: 19.13112647 Break this problem into two subproblems by setting (x + -13) equal to 19.13112647 and -19.13112647.Subproblem 1
x + -13 = 19.13112647 Simplifying x + -13 = 19.13112647 Reorder the terms: -13 + x = 19.13112647 Solving -13 + x = 19.13112647 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 = 19.13112647 + 13 Combine like terms: -13 + 13 = 0 0 + x = 19.13112647 + 13 x = 19.13112647 + 13 Combine like terms: 19.13112647 + 13 = 32.13112647 x = 32.13112647 Simplifying x = 32.13112647Subproblem 2
x + -13 = -19.13112647 Simplifying x + -13 = -19.13112647 Reorder the terms: -13 + x = -19.13112647 Solving -13 + x = -19.13112647 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 = -19.13112647 + 13 Combine like terms: -13 + 13 = 0 0 + x = -19.13112647 + 13 x = -19.13112647 + 13 Combine like terms: -19.13112647 + 13 = -6.13112647 x = -6.13112647 Simplifying x = -6.13112647Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.13112647, -6.13112647}
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