Question

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

Answer 1

ANSWER

$x =5 \pm \sqrt{35}$

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:

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

$x - 5 = \pm \sqrt{35}$

$x =5 \pm \sqrt{35}$

Answer 2

It actually has 2 answers

x =(10+√140)/2=5+√ 35 = 10.916  

or:

x =(10-√140)/2=5-√ 35 = -0.916