Question

Use completing the square to solve for x in the equation x^2-10x+25=35.

Answer 1

It actually has 2 answers

x =(10+√140)/2=5+√ 35 = 10.916

or:

x =(10-√140)/2=5-√ 35 = -0.916

Answer 2

`x =5 \pm √(35)`

Step-by-step explanation

The given quadratic equation is:

`{x}^(2) - 10x + 25 = 35`

Group the constants on the RHS,

`{x}^(2) - 10x= 35 - 25`

`{x}^(2) - 10x= 10`

Add the square of half the coefficient of x to both sides of the equation,

`{x}^(2) - 10x + ( - {5)}^(2) = 10 + ( - {5)}^(2)`

`{x}^(2) - 10x + 25= 10 + 25`

We factor the perfect square to get:

`{(x - 5)}^(2) =35`

`x - 5 = \pm √(35)`

`x =5 \pm √(35)`