To solve the quadratic equation [tex]\( x^2 - 9x - 26 = 0 \)[/tex] by completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
[tex]\[
x^2 - 9x = 26
\][/tex]
2. Identify the coefficient of the [tex]\( x \)[/tex] term, which is [tex]\(-9\)[/tex].
3. Take half of this coefficient.
[tex]\[
\text{Half of } -9 \text{ is } -\frac{9}{2}
\][/tex]
4. Square this half-coefficient to find the number that needs to be added to both sides to complete the square.
[tex]\[
\left( -\frac{9}{2} \right)^2 = \left( \frac{9}{2} \right)^2 = \frac{81}{4} = 20.25
\][/tex]
Therefore, the number that needs to be added to both sides of the equation to complete the square is [tex]\( 20.25 \)[/tex].
