Answer:
The number which number would have to be added to "complete the square" is [tex]\mathbf{(\frac{15}{2})^2 }[/tex]
Step-by-step explanation:
We need to solve the equation [tex]x^2 + 15x + 4 = 0[/tex] by completing square method.
The general form is [tex]x^2+2(x)(y)+y^2=(x+y)^2[/tex]
Solving equation using completing square method
[tex]x^2 + 15x + 4 = 0[/tex]
We would be adding and subtracting 15/2 to make it a complete square
[tex]x^2+2(1)(\frac{15}{2} )+(\frac{15}{2})^2+4-(\frac{15}{2})^2=0[/tex]
So, now it can be written in form of [tex](x+y)^2[/tex]
[tex](x+\frac{15}{2})^2+4-\frac{225}{4}=0\\(x+\frac{15}{2})^2+4-\frac{225}{4}=0\\(x+\frac{15}{2})^2+\frac{4*4-225}{4}=0\\(x+\frac{15}{2})^2+\frac{16-225}{4}=0\\(x+\frac{15}{2})^2+\frac{-209}{4}=0\\(x+\frac{15}{2})^2-\frac{209}{4}=0[/tex]
So,using the method of completing the square to solve the quadratic equation x2 + 15x + 4 = 0 we get [tex]\mathbf{(x+\frac{15}{2})^2-\frac{209}{4}=0}[/tex]
The number which number would have to be added to "complete the square" is [tex]\mathbf{(\frac{15}{2})^2 }[/tex]
