Mathematics: 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 ?

B. 2Step-by-step explanation:(4, 3) (7, 9) M = SlopeM = Slope formula Using the slope formula, plot both x and y intercepts Slope needs to be simplified into a whole number ...

If using the method of completing the square to

Ответ:

libertycooper

08.02.2022

Mathematics

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

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