Week 7 Precalc

In math, we learned how to solve a quadratic equation using the quadratic formula

x=\frac {-(b)\pm \sqrt {(b)^2-4(a)(c)}}{2a}

This method of solving will be used to solve the equation:

(2x+1)^2+4=49

before you can use the formula you first have to expand and make the right side of the equation equal zero

(2x+1)(2x+1)+4-49=0

Then foil and collect like terms

4x^2+2x+2x+1-45=0

 

4x^2+4x+1-45=0

 

4x^2+4x-44=0

from this point, you can look for a common factor to take out in order to make the equation easier. in this case, the common factor is four

x^2+x-11=0

Now you are able to use the quadratic formula to solve

A=1

B=1

C=-11

x=\frac{-(1)\pm \sqrt{(1)^2-4(1)(-11)}}{2}

 

x=\frac{-1\pm \sqrt{1+44}}{2}

 

x=\frac{-1\pm \sqrt{45}}{2}

 

x=\frac{-1\pm 3\sqrt{5}}{2}

 

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