Question

A portion of the quadratic formula proof is shown. Fill in the missing statement ( the last answer choice is (x + b/2a = + b^2-4ac/a)

Answer 1

`x+(b)/(2a)=\pm(√(b^2-4ac))/(2a)`

Explanation:

So when it says simplify the right side, all it's doing is distributing the square root across division.

So when we distribute the square root we get the fraction

`(√(b^2-4ac))/(√(4a^2))`

And it's important to know that you cannot distribute the square root across addition/subtraction, but you can with multiplication.

There's a radical identity that states:
`\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}` and this works both ways, so we can use this to combine like radicals or separate them into multiple. In this case we can separate the square root of 4a^2 into two radicals

`(√(b^2-4ac))/(√(4) * √(a^2))`

And from here it's pretty easy to see that the square root of 4 is 2, and the square root of a^2 is a, since the square exponent and square root just cancel out.

So we get the following expression on the right side

`(√(b^2-4ac))/(2a)`