Question

A portion of the Quadratic Formula proof is shown. Fill in the missing reason. A: Multiply the fractions together on the right side of the equation? B: Subtract 4ac on the right side of the equation? C: Add 4ac to both sides of the equation? D: Add the fractions together on the right side of the equation?

Answer 1

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer 2

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

$x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2}$

$\text{Consider the discriminant as }\Delta$

$\Delta=b^2-4ac$

Once we got a trinomial here, just put in factored form:

$\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2}$

$x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2}$

$x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} }$

$x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} }$

$x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a}$

$x= \frac {-b\pm \sqrt{\Delta}}{2a}$

$x= \frac {-b\pm \sqrt{b^2-4ac}}{2a}$