Given the expression below
[tex]x^2+10x-13=0[/tex]
The general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]
Using the completing the square method,
[tex]\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}[/tex]
Where b =10 from the given equation
[tex]\begin{gathered} \text{Addding (}\frac{b}{2})^2\text{ to both sides} \\ ie\text{ (}\frac{10}{2})^2=5^2=25 \\ \text{Add 25 to both sides} \end{gathered}[/tex][tex]x^2+10x+25=13+25[/tex]
For part A, the numerical value to be added is 25
Hence, for part A, the answer is 25-25
By completing the square
[tex]\begin{gathered} x^2+10x+25=13+25 \\ (x+5)^2=38 \\ (x+5)^2-38=0 \end{gathered}[/tex]
Hence, for part B, the answer is (x+5)²-38
