Question

Solve for w.
4w²+3=-13w

Answer 1

1/4

Explanation:

w = (-13 ± √(169 - 48)) / 8

w = (-13 ± √121) / 8

w = (-13 ± 11) / 8

This gives us two possible solutions:

w₁ = (-13 + 11) / 8 = -2 / 8 = -1/4

So, the solutions for w are -1/4

To verify these solutions, we can substitute them back into the original equation:

For w = -1/4:

4(-1/4)² + 3 = -13(-1/4)

1/4 + 3 = 13/4

13/4 = 13/4 (True)

Therefore, the solutions -1/4 and are correct.

Answer 2

`\sf w = -3 \ ; (-1)/(4)`

Explanation:

Write the quadratic equation in standard form: ax² + bx + c = 0

4w² + 3 = -13w

4w² + 13w + 3 = 0

Product =3*4 = 12

Sum = 13

Factors = 1 , 12

When we multiply 1*12, we get 12 and when we add 1 +12, we get 13.

Rewrite the middle term using the factors.

4w² + 12w + w + 3 = 0

Take the common term 4w from the first two terms.

4w*(w + 3) + (w + 3) = 0

(w +3)(4w + 1) = 0

w + 3 = 0 ; 4w + 1 =0

w = -3 ; 4w = -1

`\sf w = (-1)/(4)`

Anwer:

`\bf w = -3 ; (-1)/(4)`