Question

Solve for w. −16w-3 = 5w²

Answer 1

Answer:

w = -1/5

OR

w = -3

Step-by-step 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:

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

Answer 2

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

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