Question

Consider the equation: 24=x^2 - 4x + 31) Rewrite the equation by completing the square.Your equation should look like (x + c)^2 = d or (x – c)^2 = d.

Answer 1

(x-2)^2=25

Step-by-step explanation:

Given the below quadratic equation;

`x^2-4x+3=24`

To rewrite by completing the square, the 1st step is to subtract 3 from both sides of the equation;

`\begin{gathered} x^2-4x+3-3=24-3 \\ x^2-4x=21 \end{gathered}`

The 2nd step is to add half of the coefficient of x squared to both sides of the equation;

`\begin{gathered} x^2-4x+(-_{}(1)/(2)\ast4)^2=21+(-(1)/(2)\ast4)^2 \\ x^2-4x+(-2)^2=21+(-2)^2 \\ x^2-4x+4=21+4 \\ x^2-4x+4=25 \end{gathered}`

We can then factor the perfect square as;

`(x-2)^2=25_{}`

To find the solutions of the equation, we have to take the square root of both sides of the equation;

`\begin{gathered} \sqrt[]{(x-2)^2}=\sqrt[]{25} \\ x-2=(+)/(-)5 \end{gathered}`

For x 1;

`x_1=+5+2=7`

For x2;

`x_2=-5+2=-3_{}`

So x1 = 7 and x2 = -3.