Solving Quadric Equations

Question

Use the Quadric formula to solve the equation.

x^2 + 4x + 29 =0

Answer 1

Complete the square:

x^2 + 4x +29 = 0 -> x^2+4x = -29

=> note: (4/2)^2=4

x^2 +4x +4 = -29 +4

(x+2)^2 = -25

x+2 = +5i and x+2 = -5i

x= 5i +2 , -5i-2

Quadratic equation:

x= -b ± √(b^2 - 4ac) / 2a

x = -4 ± √(16 - 116) / 2

x = -4 ± √(-100) / 2

x = -4 ± 10i / 2

x = -2 ± 5i

Answer 2

You want to plug in values from the equation into the quadratic formula.

So we need values for a, b and c.

a comes from the coefficient for x^2

b comes from the coefficient for x

and c is the last numerical value

Once you know a, b and c, you can plug these values into the quadratic formula!

Answer 3

A=1 B=4 C=29

B^2 - 4AC = 4^2 - 4(1)(29) = 16 - 116 = -100

x = [-4 +or- sqrt(-100)] / 2

= [-4 +or- 10i]/2

= -2 +or- 5i

check

x = -2+5i

x^2 = (4 -20i - 25)

= -21 - 20i

x^2 + 4x = -21 - 20i + -8 + 20i = -29

yes it checks

x = -2 +or- 5i