Question

The steps to derive the quadratic formula are shown below:

Answer 1

Answer:

  (c)  x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

Step-by-step explanation:

The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.

Result so far

The last step shown in the derivation so far is ...

  $x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}$

Next step

The left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.

  $\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}$

Answer 2

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

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

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

So, taking the square root of both sides,

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