Question

If using the method of completing the square to solve the quadratic equation x^2 - 9x - 8 = 0, which number would have to be added to "complete the square"

Answer 1

Answer:

Number: 28.25

Solution to Quadratic: $x=\frac{9}{2}\pm\frac{\sqrt{113}}{2}}$

Step-by-step explanation:

$x^2-9x-8=0$

$x^2-9x-8+28.25=0+28.25$ <-- 28.25 is the number you need to add

$x^2-9x+20.25=28.25$

$(x-4.5)^2=28.25$

$x-4.5=\pm\sqrt{28.25}$

$x=4.5\pm\sqrt{28.25}$

$x=\frac{9}{2}\pm\sqrt{\frac{113}{4}}$

$x=\frac{9}{2}\pm\frac{\sqrt{113}}{2}}$