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Simplifying x2 + -26x = 2450 Reorder the terms: -26x + x2 = 2450 Solving -26x + x2 = 2450 Solving for variable 'x'. Reorder the terms: -2450 + -26x + x2 = 2450 + -2450 Combine like terms: 2450 + -2450 = 0 -2450 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2450' to each side of the equation. -2450 + -26x + 2450 + x2 = 0 + 2450 Reorder the terms: -2450 + 2450 + -26x + x2 = 0 + 2450 Combine like terms: -2450 + 2450 = 0 0 + -26x + x2 = 0 + 2450 -26x + x2 = 0 + 2450 Combine like terms: 0 + 2450 = 2450 -26x + x2 = 2450 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 = 2450 + 169 Reorder the terms: 169 + -26x + x2 = 2450 + 169 Combine like terms: 2450 + 169 = 2619 169 + -26x + x2 = 2619 Factor a perfect square on the left side: (x + -13)(x + -13) = 2619 Calculate the square root of the right side: 51.176166328 Break this problem into two subproblems by setting (x + -13) equal to 51.176166328 and -51.176166328.Subproblem 1
x + -13 = 51.176166328 Simplifying x + -13 = 51.176166328 Reorder the terms: -13 + x = 51.176166328 Solving -13 + x = 51.176166328 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 = 51.176166328 + 13 Combine like terms: -13 + 13 = 0 0 + x = 51.176166328 + 13 x = 51.176166328 + 13 Combine like terms: 51.176166328 + 13 = 64.176166328 x = 64.176166328 Simplifying x = 64.176166328Subproblem 2
x + -13 = -51.176166328 Simplifying x + -13 = -51.176166328 Reorder the terms: -13 + x = -51.176166328 Solving -13 + x = -51.176166328 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 = -51.176166328 + 13 Combine like terms: -13 + 13 = 0 0 + x = -51.176166328 + 13 x = -51.176166328 + 13 Combine like terms: -51.176166328 + 13 = -38.176166328 x = -38.176166328 Simplifying x = -38.176166328Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.176166328, -38.176166328}
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