Question

Find the solution set of the following quadratic equations by completing the square.

1.) x^2 - 10x + 1 = 0
2.) 4x^2 - 8x = 12

​

Answer 1

1)
`\bold{x=2\sqrt6+5\quad\ \vee\quad x=-2\sqrt6+5}`

2)
`\bold{x=3\quad\vee\quad x=-1}`

Explanation:

1)

`x^2 - 10x + 1 = 0\\\\x^2 - 2\cdot x\cdot5 +5^2-5^2 + 1 = 0\\\\(x-5)^2-25+1=0\\\\(x-5)^2=24\\\\x-5=√(24)\qquad\vee\qquad x-5=-√(24)\\\\ x=2\sqrt6+5\qquad\vee\qquad x=-2\sqrt6+5`

2)

`4x^2-8x=12\\\\x^2-2x=3\\\\x^2-2\cdot x\cdot1+1^2-1^2=3\\\\(x-1)^2-1=3\\\\(x-1)^2=4\\\\x-1=2\qquad\vee\qquad x-1=-2\\\\x=3\qquad\vee\qquad x=-1`