Question

Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms.

16x² - 25 = 0
Answer
Separate multiple values with a comma.
X
11

Answer 1

x = -
`(5)/(4)` , x =
`(5)/(4)`

Explanation:

given

16x² - 25 = 0 ← 16x² - 25 is a difference of squares and factors in general as

• a² - b² = (a + b)(a - b)

Then

16x² - 25

= (4x)² - 5²

= (4x + 5)(4x - 5) ← in factored form

the equation can now be expressed in factored form as

16x² - 25 = 0

(4x + 5)(4x - 5) = 0

equate each factor to zero and solve for x

4x + 5 = 0 ( subtract 5 from both sides )

4x = - 5 ( divide both sides by 4 )

x = -
`(5)/(4)`

4x - 5 = 0 ( add 5 to both sides )

4x = 5 ( divide both sides by 4 )

x =
`(5)/(4)`

solutions are x = -
`(5)/(4)` , x =
`(5)/(4)`