Question

Solve the quadratic by quadratic formula below

a^2-4a=21

Answer 1

`a = -3, a = 7`

Explanation:

Hello!

Standard form of a Quadratic:
`ax^2 + bx +c = 0`

We have to solve the quadratic by factoring and using the zero product property.

First, convert it to standard form.

• 
  `a^2 - 4a = 21`
• 
  `a^2 - 4a - 21 = 0`

Now, find two numbers that add up to -4, but multiply to -21. The numbers that work are -7 and 3. Expand -4a to -7a and 3a.

Factor by grouping

• 
  `a^2 - 4a - 21 = 0`
• 
  `a^2 - 7a + 3a -21 = 0`
• 
  `a(a - 7)+3(a - 7) = 0`
• 
  `(a +3 )(a - 7) = 0`
• 
  `a = -3, a = 7`

The solutions for a are -3 and 7.

Answer 2

a^2 – 4a = 21

by trasponsing 21 to the left:

a^2 – 4a – 21 = 0

by quadratic formula:

x = [- (-4) ± sqrt [(- 4)^2 – 4 (1) (-21)]] / 2 (1)

x = [4 ± sqrt (100)] / 2

x = [4 ± 10] / 2

x = -3, 7