Question

Complete the square to solve the equation below.check all that apply. x2 - 10x - 1 = 13

Answer 1

x² -10x -1 = 13
x² -10x = 14
x² -10x +25 = 39 . . . . . add (10/2)² to complete the square
(x -5)² = 39
x -5 = ±√39
x = 5 ±√39

Answer 2

Answer:

Complete square: $(x-5)^2=39$

Solutions: $x=5\pm\sqrt{39}$

Step-by-step explanation:

We have been given an equation $x^2-10x-1=13$. We are asked to complete the square.

First of all, we will add 1 to both sides of our given equation.

$x^2-10x-1+1=13+1$

$x^2-10x=14$

Now we will add $(\frac{b}{2})^2$ to both sides of our equation. We can see that the value of b is 10.

$(\frac{10}{2})^2=5^2=25$

Upon adding 25 on both sides of our equation we will get,

$x^2-10x+25=14+25$  

$x^2-10x+25=39$

$(x-5)^2=39$

Taking square root of both sides we will get,

$(x-5)=\sqrt{39}$

$(x-5)=\pm\sqrt{39}$

$x-5=\pm\sqrt{39}$

Adding 5 on both sides of our equation we will get.

$x-5+5=5\pm\sqrt{39}$

$x=5\pm\sqrt{39}$

Therefore, solutions for our given equation are $x=5\pm\sqrt{39}$.