Question

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

Answer 1

Answer:

$x = 5 + \sqrt{35} \: \: \:or \: \: \: x = 5 - \sqrt{35}$

Step-by-step 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

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

We have the final answer as

$x = 5 + \sqrt{35} \: \: \:or \: \: \: x = 5 - \sqrt{35}$

Hope this helps you