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Simplifying x2 + -26x + 26 = 0 Reorder the terms: 26 + -26x + x2 = 0 Solving 26 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -26x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -26x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -26x + x2 = 0 + -26 -26x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -26x + x2 = -26 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 = -26 + 169 Reorder the terms: 169 + -26x + x2 = -26 + 169 Combine like terms: -26 + 169 = 143 169 + -26x + x2 = 143 Factor a perfect square on the left side: (x + -13)(x + -13) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (x + -13) equal to 11.958260743 and -11.958260743.Subproblem 1
x + -13 = 11.958260743 Simplifying x + -13 = 11.958260743 Reorder the terms: -13 + x = 11.958260743 Solving -13 + x = 11.958260743 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 = 11.958260743 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.958260743 + 13 x = 11.958260743 + 13 Combine like terms: 11.958260743 + 13 = 24.958260743 x = 24.958260743 Simplifying x = 24.958260743Subproblem 2
x + -13 = -11.958260743 Simplifying x + -13 = -11.958260743 Reorder the terms: -13 + x = -11.958260743 Solving -13 + x = -11.958260743 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 = -11.958260743 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.958260743 + 13 x = -11.958260743 + 13 Combine like terms: -11.958260743 + 13 = 1.041739257 x = 1.041739257 Simplifying x = 1.041739257Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.958260743, 1.041739257}
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