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Simplifying x2 + -26x + 98 = 0 Reorder the terms: 98 + -26x + x2 = 0 Solving 98 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + -26x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + -26x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -26x + x2 = 0 + -98 -26x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 -26x + x2 = -98 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 = -98 + 169 Reorder the terms: 169 + -26x + x2 = -98 + 169 Combine like terms: -98 + 169 = 71 169 + -26x + x2 = 71 Factor a perfect square on the left side: (x + -13)(x + -13) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -13) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -13 = 8.426149773 Simplifying x + -13 = 8.426149773 Reorder the terms: -13 + x = 8.426149773 Solving -13 + x = 8.426149773 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 = 8.426149773 + 13 Combine like terms: -13 + 13 = 0 0 + x = 8.426149773 + 13 x = 8.426149773 + 13 Combine like terms: 8.426149773 + 13 = 21.426149773 x = 21.426149773 Simplifying x = 21.426149773Subproblem 2
x + -13 = -8.426149773 Simplifying x + -13 = -8.426149773 Reorder the terms: -13 + x = -8.426149773 Solving -13 + x = -8.426149773 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 = -8.426149773 + 13 Combine like terms: -13 + 13 = 0 0 + x = -8.426149773 + 13 x = -8.426149773 + 13 Combine like terms: -8.426149773 + 13 = 4.573850227 x = 4.573850227 Simplifying x = 4.573850227Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.426149773, 4.573850227}
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