How do I solve this equation? Please explain and do step by step.
6m squared -5m-14=0
6m^2 - 5m - 14 = 0
it's mainly trial and error. Since 5 is a relatively small number, don't expect to see factors like (6m+1)(m-14)
I'd try (3m-?)(2m+?)
(3m-)(2m+) Hmm. nope
(6m-7)(m+2) = 6m^2 + 5m - 14
close, but we need -5m. So,
(6m+7)(m-2)
Then you have to set each factor equal to zero and solve for m.
I actually have another way to factor instead of trial and erro.
you multiply the 6 times -14 to get -84
Then you think of a two numbers that multiply to =-84 and add up to be -5
They are -12 plus 7
rewrite as 6m^2 -12m + 7m -14
group (6m^2 -12m) + (7m -14)
take out common factors
6m(m -2) + 7 (m-2)
factor out the m-2
and you have (6m+7)(m-2)
It is a newer methos and eliminates the guessing. It works every time.
how do I solve (16)^3 +48(16)^2
To solve the given equation, 6m^2 - 5m - 14 = 0, we can use the quadratic formula. The quadratic formula is used to find the values of m that satisfy a quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants.
Step 1: Identify the coefficients of the quadratic equation
In this equation, the coefficients are:
a = 6
b = -5
c = -14
Step 2: Plug the coefficients into the quadratic formula
The quadratic formula is given as:
m = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values from our equation:
m = (-(-5) ± √((-5)^2 - 4 * 6 * (-14))) / (2 * 6)
Step 3: Simplify the equation
Simplifying the equation further, we get:
m = (5 ± √(25 + 336)) / 12
m = (5 ± √361) / 12
Step 4: Evaluate the square root
√361 = 19 (as 19^2 = 361)
Step 5: Substitute the value back into the formula
We have two possible values for m:
m = (5 + 19) / 12
m = 24 / 12
m = 2
m = (5 - 19) / 12
m = -14 / 12
m = -7 / 6
Therefore, the two solutions to the equation 6m^2 - 5m - 14 = 0 are:
m = 2
m = -7/6