How do you solve [tex]x^2 - 10x + 9 = 0[/tex] by completing the square?

x 2 − 10 x + 9 = 0 ( ∗ ) x 2 − 2 x ⋅ 5 + 5 2 ​ ​ − 5 2 + 9 = 0 ( x − 5 ) 2 − 25 + 9 = 0 ( x − 5 ) 2 − 16 = 0 / + 16 ( x − 5 ) 2 = 16 ⟺ x − 5 = − 16 ​ ∨ x − 5 = 16 ​ x − 5 = − 4 ∨ x − 5 = 4 x = − 4 + 5 ∨ x = 4 + 5 x = 1 ∨ x = 9
( ∗ ) ( a − b ) 2 = a 2 − 2 ab + b 2

Answered by Anonymous | 2024-06-10

x 2 − 10 x + 9 = 0 x 2 − 2 ⋅ 5 x + 5 2 − 5 2 + 9 = 0 ( x − 5 ) 2 − 25 + 9 = 0 ( x − 5 ) 2 = 16 x − 5 = 4 ∨ x − 5 = − 4 x = 9 x = 1

Answered by kate200468 | 2024-06-10

To solve x 2 − 10 x + 9 = 0 by completing the square, move the constant to the other side, complete the square, and solve for x. The solutions are x = 9 and x = 1 . This method involves manipulating the equation into a perfect square form, making it easier to solve.
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Answered by Anonymous | 2024-12-20