How do you solve #m^ { 2} + 12m + 71= 0#?
2 Answers
Refer to the explanation for the process.
Explanation:
Solve:
where:
Use the quadratic formula to solve for
Plug in the known values.
Simplify.
Prime factorize
Simplify.
Reduce.
Solutions for
there is no solution for any real number m to solve the equation.
Explanation:
we usually we can factor out the equation make it look like (a-x)(b-x)=0, the solve for the two x's.
But since it doesn't seem as an obvious whole number, we can resort to solving it via the quadratic formula:
the general expression is:
we have:
so: a=1, b=12, c=71
now plug in the formula,
the problem here, is that we know for all real numbers, anything under a square root, or a root in general must be equal or greater than zero, but if we take a closer look to what's under the root, we find it -140
which would result into an error on your calculator, or would show up an answer (if it had that button to solve directly) two answers which are: 0.85+3.06i and 0.85-3.06i. These are complex numbers, that are not contained within the real numbers.
So if you are solving in the reals (m is a real number) then, there is no solution for the equation.
if you are solving in the complex numbers, which i assume you are studying a unit about, then those are your two answers, message me if you want details.