Question

Solve for w.
−16w-3 = 5w²

Answer 1

`- 16w - 3 = 5 {w}^(2) \\ \\ 0 = 5 {w}^(2) + 16w + 3 \\ \\ 5 {w}^(2) + 16w + 3 = 0 \\ \\ 5 {w}^(2) + w + 15w + 3 = 0 \\ \\ (5 {w}^(2) + w) + (15w + 3) = 0 \\ \\ w(5w + 1) + 3(5w + 1) = 0 \\ \\ (w + 3)(5w + 1) = 0.`

The value of w is -3 and -1/5 .

Answer 2

w = -1/5

OR

w = -3

Explanation:

Given equation:

−16w-3 = 5w²

Solution:

Subtracting 5w^2 from both sides,we get

• -16w-3-5w² = 5w² - 5w²
• -5w²-16w-3=0

Factor the LHS of this equation using middle term factor:

• (-5w²-1)(w-3)

Now,

• 
  `( - 5w - 1) = 0 \: \: \: \: \: \: \: \: ...(1)`
• 
  `(w - 3) = 0 \: \: \: \: \: \: \: \: \: \: ... (2)`

Solving for equation 1:

• 
  `- 5w = 0 + 1`
• 
  `- 5w = 1`
• 
  `\boxed{w = - \cfrac{1}{5} }`

Solving for equation 2:

• 
  `w - 3 = 0`
• 
  `w = 0 - 3`
• 
  `\boxed{w = - 3}`