Question

8w^2-w-7= 0
Write your answers as integers,proper, or improper

Answer 1

w = -
`(7)/(8)`, w = 1

Explanation:

Given

8w² - w - 7 = 0

Consider the factors of the product of the w² term and the constant term which sum to give the coefficient of the w- term.

product = 8 × - 7 = - 56 and sum = - 1

The factors are - 8 and + 7

Use these factors to split the w- term

8w² - 8w + 7w - 7 = 0 ( factor the first/second and third/fourth terms )

8w(w - 1) + 7(w - 1) ← factor out (w - 1) from each term

(w - 1)(8w + 7) = 0

Equate each factor to zero and solve for w

8w + 7 = 0 ⇒ 8w = - 7 ⇒ w = -
`(7)/(8)`

w - 1 = 0 ⇒ w = 1

Answer 2

x = 1, -7/8

Explanation:

Equation: 8w^2 - w 7 = 0

Factor: (x - 1)(8x + 7) = 0

Solve for 0: x - 1 + 1 = 0 + 1 -> x = 1

8x / 8 + 7 - 7 = 0 - 7 / 8 -> x = -7/8