Question

If using the method of completing the square to solve the quadratic equation x2 + 15x + 4 = 0, which number would have to be added to "complete the square"?​

Answer 1

Answer:

The number which number would have to be added to "complete the square" is $\mathbf{(\frac{15}{2})^2 }$

Step-by-step explanation:

We need to solve the equation $x^2 + 15x + 4 = 0$ by completing square method.

The general form is $x^2+2(x)(y)+y^2=(x+y)^2$

Solving equation using completing square method

$x^2 + 15x + 4 = 0$

We would be adding and subtracting 15/2 to make it a complete square

$x^2+2(1)(\frac{15}{2} )+(\frac{15}{2})^2+4-(\frac{15}{2})^2=0$

So, now it can be written in form of $(x+y)^2$

$(x+\frac{15}{2})^2+4-\frac{225}{4}=0\\(x+\frac{15}{2})^2+4-\frac{225}{4}=0\\(x+\frac{15}{2})^2+\frac{4*4-225}{4}=0\\(x+\frac{15}{2})^2+\frac{16-225}{4}=0\\(x+\frac{15}{2})^2+\frac{-209}{4}=0\\(x+\frac{15}{2})^2-\frac{209}{4}=0$

So,using the method of completing the square to solve the quadratic equation x2 + 15x + 4 = 0 we get  $\mathbf{(x+\frac{15}{2})^2-\frac{209}{4}=0}$

The number which number would have to be added to "complete the square" is $\mathbf{(\frac{15}{2})^2 }$