Question

Hello, I need helping solving for x by completing the square.

Answer 1

Step-by-step explanation:

Given;

We are given the quadratic equation as shown below;

`x^2-8x+13=0`

Required;

We are required to solve for x by completing the square method.

Step-by-step solution;

We start with the constant 13.

Subtract 13 from both sides of the equation;

`x^2-8x+13-13=0-13`
`x^2-8x=-13`

Next we take the coefficient of x (that is -8). We half it, and then square the result. After that we add it to both sides of the equation;

`\begin{gathered} (1)/(2)*-8=-(8)/(2) \\ Next: \\ (-(8)/(2))^2 \end{gathered}`

We now have;

`x^2-8x+(-(8)/(2))^2=-13+(-(8)/(2))^2`

We can now simplify this;

`x^2-8x+(-4)^2=-13+(-4)^2`
`x^2-8x+16=-13+16`
`x^2-8x+16=3`

We now factorize the left side of the equation;

`\begin{gathered} x^2-4x-4x+16 \\ (x^2-4x)-(4x-16) \\ x(x-4)-4(x-4) \\ (x-4)(x-4) \\ Therefore: \\ (x-4)^2 \end{gathered}`

we can now refine our equation to become;

`(x-4)^2=3`

We can now solve for x as follows;

Take the square root of both sides;

`x-4=\pm√(3)`

Therefore;

`\begin{gathered} x-4=√(3) \\ x=√(3)+4 \\ Also: \\ x-4=-√(3) \\ x=-√(3)+4 \end{gathered}`

ANSWER:

`\begin{gathered} x_1=4+√(3) \\ x_2=4-√(3) \end{gathered}`