In this unit we learned how to factor trinomials, complete the square, and the quadratic formula in order to find the x intercepts. With completing the square and the quadratic formula there was many places where you could make silly mistakes so it was best to go slow while really thinking.
I will be explaining completing the square, I struggled with completing the square the most out of the three different ways to solve for x. There can be fractions which was where I made the most mistakes. So the steps to complete the square are fairly simple. with an equation like x²+2x+4=0 you need to first divide the second term by 2 after dividing the second term by 2 you need to square the quotient and make a 0 pair.
so in this case: (x²+2x+1-1)+4=0
Then you have to start isolating x: (x+1)²+3=0 —> (x+1)² = -3
Then you square root both sides to get rid of the exponent, which makes the equation: x+1= +-√-3
In this case the number under the square root is a negative so it is impossible to do because there are no real roots. I stopped there because I noticed the negative but if it were a positive you would isolate x by subtracting the 1 and moving it to the other side. Then you would proceed to solve the equation.
Now if there was a leading coefficient greater than 1 than you have to divide everything by the leading coefficient to get x by it self.
ex: 2x²+4x+10=0 —–> x²+2x+5=0
Then you do the same process as I showed earlier