How do you solve x^2 – 3x = 4x – 1 using the quadratic formula?

1 Answer
ProfLayton
Apr 17, 2016

First, we have to move everything to the left so it resembles this form: ax^2+bx+c=0, also known as the standard form.

For this case, all we have to do is move everything to 1 side (it doesn't matter which side, although I prefer to move it all to the side with x^2 already in it)

x^2-3x=4x-1
x^2-7x+1=0

Now you will need to know the quadratic formula to solve this problem: x=(-b+-sqrt(b^2-4ac))/(2a)

But what are a, b, and c you ask? Well that's why we rearranged the original equation. a is the number next to x^2, b is the number next to x, and c doesn't have an x next to it. Doing this, we find a=1, b=-7, c=1. All we have to do is put into the quadratic formula and simplify:

x=(-(-7)+-sqrt((-7)^2-4(1)(1)))/(2(1))
x=(7+-sqrt(49-4))/(2)
x=(7+-sqrt(45))/(2)

So this gives us two answers:
x=(7+sqrt(45))/(2) or (7-sqrt(45))/(2)
Which are the correct answers.

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