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

Combine numerators over the common denominator to make one term

Explanation:

Answer 2

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

Explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

`$x^2+(b)/(a) x+\left((b)/(2a) \right)^2=(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+(b)/(2a)\right)^2=(\Delta)/(4a^2) $`

`$x+(b)/(2a)=\pm(\Delta)/(4a^2) $`

`$x+(b)/(2a)=\pm \sqrt{(\Delta)/(4a^2) } $`

`$x=-(b)/(2a)\pm \sqrt{(\Delta)/(4a^2) } $`

`$x=-(b)/(2a)\pm ( √(\Delta) )/(2a) $`

`$x= \frac {-b\pm √(\Delta)}{2a} $`

`$x= \frac {-b\pm √(b^2-4ac)}{2a} $`