Answer :
To complete the square for the equation \( x^2 - 6x = 5 \), follow these steps:
1. Identify the coefficient of \( x \): Here, the coefficient of \( x \) is \(-6\).
2. Divide the coefficient of \( x \) by 2:
[tex]\[ -6 \div 2 = -3 \][/tex]
3. Square the result from step 2:
[tex]\[ (-3)^2 = 9 \][/tex]
4. Add this squared value to both sides of the equation:
[tex]\[ x^2 - 6x + 9 = 5 + 9 \][/tex]
Thus, the number that should be added to both sides of the equation to complete the square is [tex]\( 9 \)[/tex].
1. Identify the coefficient of \( x \): Here, the coefficient of \( x \) is \(-6\).
2. Divide the coefficient of \( x \) by 2:
[tex]\[ -6 \div 2 = -3 \][/tex]
3. Square the result from step 2:
[tex]\[ (-3)^2 = 9 \][/tex]
4. Add this squared value to both sides of the equation:
[tex]\[ x^2 - 6x + 9 = 5 + 9 \][/tex]
Thus, the number that should be added to both sides of the equation to complete the square is [tex]\( 9 \)[/tex].
