(Make sure to set f(x) to zero)
For this, I will be completing the square. Firstly, add 20 to both sides of the equation: [tex]20=4x^2+16x[/tex]
Next, divide both sides by 4: [tex]5=x^2+4x[/tex]
Next, we want to make the right side of the equation a perfect square. To do that, divide the x coefficient by 2 and square that quotient. In this case:
4 ÷ 2 = 2, 2² = 4
Add four to both sides of the equation: [tex]9=x^2+4x+4[/tex]
Next, factor the right side of the equation: [tex]9=(x+2)^2[/tex]
Next, square root both sides of the equation: [tex]\pm 3=x+2[/tex]
Lastly, subtract 2 to both sides of the equation and your answers are:
[tex]-2\pm 3=x\\1,-5=x[/tex]
