w^2-3w-40=0 how are you supposed to solve this and how do you find the solution for w
I see very simple factors here
(w-8)(w+5) = 0
take it from here
what about the 3w though? where does that go and how do you figure to get the numbers on the oposite side, sorry I just don't understand math
(w-8)(w+5)
using the distributive property of multipication this is
w(w+5) -8(w+5)
= w^2 + 5 w - 8 w - 40
see , you have +5w-8w = -3w
Now, we want to know when
(w-8)(w+5) is zero
well that is if w = 8
or if w = -5
GIVEN: W^2 - 3W -40 = 0
Factor the equation into 2 binomials:
( W + 5 ) ( W - 8 ) = 0.
To check the factored equation,
multiply W in the first parenthesis by
each term in the 2nd parenthesis.Then,
multiply 5 in the first parenthesis by
each term in the 2nd parenthesis:
W^2 - 8W + 5W - 40 = 0.
Combine like-terms:
W^2 - 3W - 40 = 0. Checked OK.
Return to factored equation:
( W + 5 ) ( W - 8 ) = 0.
Solve for W.
If w + 5 = 0, W = - 5; If W - 8 = 0,
W = 8.
Solutions: W = -5 and W = 8.
A 2nd degree (W^2) equation has a
maximum of 2 solutions.
To solve the quadratic equation w^2 - 3w - 40 = 0, you can use the quadratic formula or factorization method.
1. Quadratic Formula method:
The quadratic formula is given by w = (-b ± √(b^2 - 4ac)) / (2a), where the equation is in the form ax^2 + bx + c = 0.
In this case, a = 1, b = -3, and c = -40.
Substituting these values into the quadratic formula, we get:
w = (-(-3) ± √((-3)^2 - 4(1)(-40))) / (2(1))
Simplifying further:
w = (3 ± √(9 + 160)) / 2
w = (3 ± √169) / 2
w = (3 ± 13) / 2
So, we have two possible solutions for w:
w1 = (3 + 13) / 2 = 16 / 2 = 8
w2 = (3 - 13) / 2 = -10 / 2 = -5
Therefore, the solutions to the equation w^2 - 3w - 40 = 0 are w = 8 and w = -5.
2. Factoring method:
If the equation can be factored, it can be solved by setting each factor equal to zero.
w^2 - 3w - 40 = 0 can be factored as (w - 8)(w + 5) = 0
Setting each factor equal to zero:
w - 8 = 0 or w + 5 = 0
Solving these equations gives:
w = 8 or w = -5
So, the solutions obtained from factoring are w = 8 and w = -5, which is the same as the solutions obtained using the quadratic formula.