Question

Solve for x in the equation x^2- 10x+ 25=35

Answer 1

`x = 5 + √(35) \: \: \:or \: \: \: x = 5 - √(35) \\`

Explanation:

x² - 10x + 25 = 35

Move 35 to the left side of the equation

That's

x² - 10x + 25 - 35 = 0

x ² - 10x - 10 = 0

Using the quadratic formula solve the equation

That's

`x = \frac{ - b\pm \sqrt{ {b}^(2) - 4ac } }{2a}`

From the question

a = 1 , b = - 10 , c = - 10

Substitute the values into the above formula and solve

That's

`x = \frac{ - - 10\pm \sqrt{( { - 10})^(2) - 4(1)( - 10) } }{2(1)} \\ = (10\pm √(100 + 40) )/(2) \\ = (10\pm √(140) )/(2) \\ = (10\pm2 √(35) )/(2) \\ = (10)/(2) \pm (2 √(35) )/(2) \\ = 5\pm √(35)`

We have the final answer as

`x = 5 + √(35) \: \: \:or \: \: \: x = 5 - √(35) \\`

Hope this helps you