Quadratic Formula

Algebra 1 Tutorial

Quadratic Formula


The quadratic formula is a life-saver when finding the value(s) for a variable given a complex equation. The formula itself may seem overwhelming, but the process is as simple as plugging in the numbers that are given to you from the original equation into the quadratic formula.

Sample Problem

Lets say you are asked to solve for “x” when given the equation 5(x^2)+4x=3
[I want to clarify, (x^2) is read as “x squared” or “x to the second.”]


There is no easy way to get the variable “x” all by itself, so lets use the Quadratic Formula.

The first step when using the quadratic formula is to set the equation equal to zero. In order for us to do that, we must subtract 3 to each side of the equal sign. We do this because there is a positive 3 where a zero is supposed to be. By subtracting 3, we get the zero that we want, but we must subtract 3 to both sides of the equal sign.

The result is 5(x^2)+4x-3=o

Now we can use the Quadratic Formula. I will use “{ }” to indicate what goes under the square root. The Quadratic Formula is x=(-b+{(b^2)-4ac})/2a and x=(-b-{(b^2)-4ac})/2a
There are two formulas presented, the only difference is adding the square root or subtracting the square root.

looking at the quadratic formula,
a= the coefficient of the term with “x” being squared, in our case, a=5
b= the coefficient of the term with “x”, in our case, b=4
c= the term without a variable, in our case, c=-3

Now, plug a, b, and c into the quadratic formulas. Do one formula at a time, but don’t forget to do both. You will always get 2 answers, they won’t always match, but sometimes they do.

Your 2 x-values from the quadratic formula should be x=-1.2717797887 and x=0.4717797887

You have to check which x-values are correct. You can do that by plugging in the first x-value (x=-1.2717797887) into your equation; 5(x^2)+4x-3=0
If you plug the x-value in and you get 0=0, then that x-value is the correct answer.

The x-values that give us 0=0 is only x=0.4717797887
Therefore, the answer is x=0.4717797887
I hope this helped!

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