solve equation by factoring 3m^2-8m=35
I need to show full work as well please help
Bring the 35 to the Left hand side, then use the quadratic equation (if you cant find the factors in an easier way).
You start it, I can fill in your blanks : )
3m^2 - 8m - 35 = 0,
A*C = 3*(-35) = -105 = 7 * (-15),
Choose the set of factors whose sum = -8.
3m^2 + (7m - 15m) - 35 = 0,
(3m^2 + 7m) + (-15m - 35) = 0,
m(3m + 7) - 5(3m + 7) = 0,
(3m + 7)(m - 5) = 0,
3m + 7 = 0, m = -7/3.
m-5 = 0, m = 5.
To solve the equation 3m^2 - 8m = 35 by factoring, follow these steps:
Step 1: Move all terms to one side to set the equation to zero.
3m^2 - 8m - 35 = 0
Step 2: Find two numbers that multiply to give the product of the coefficient of the squared term (3) and the constant term (-35), and sums to give the coefficient of the linear term (-8).
In this case, the numbers are -5 and 7, since (-5) * 7 = -35 and (-5) + 7 = -8.
Step 3: Rewrite the middle term (-8m) into two separate terms using the two numbers found in step 2.
3m^2 - 5m + 7m - 35 = 0
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
(3m^2 - 5m) + (7m - 35) = 0
m(3m - 5) + 7(3m - 5) = 0
Step 5: Notice that both pairs have a common binomial, (3m - 5). Factor it out.
(m + 7)(3m - 5) = 0
Step 6: Set each factor equal to zero and solve for m.
m + 7 = 0 or 3m - 5 = 0
For the first equation (m + 7 = 0), subtract 7 from both sides of the equation:
m = -7
For the second equation (3m - 5 = 0), add 5 to both sides and then divide by 3:
3m = 5
m = 5/3
Therefore, the solutions to the equation 3m^2 - 8m = 35 are m = -7 and m = 5/3.