Question

How do you solve \[3{{m}^{2}}+7=301\]?

Answer 1

Hint: In this problem, we have to solve and find the value of m from the given equation, we can first subtract the number 7 on both the left-hand side and the right-hand side of the equation in order to keep the terms with variable in one side and the constant terms in the other side for further simplification. We can divide by number 3 on both sides and we can take square root on both sides. We can then simplify the terms inside the root to get the value of m.

Complete step by step answer:
We know that the given equation to be solved is,
\[3{{m}^{2}}+7=301\]
We can subtract the number 7 on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow 3{{m}^{2}}+7-7=301-7\]
We can simplify the above step, we get
\[\Rightarrow 3{{m}^{2}}=294\]
We can now divide the number 3 on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow {{m}^{2}}=\dfrac{294}{3}=98\]
We can now take square root on both sides, we get
\[\Rightarrow m=\pm \sqrt{98}\]
Now we can simplify the term inside the root, we get
\[\Rightarrow m=\pm \sqrt{2\times 7\times 7}=\pm 7\sqrt{2}\]
Therefore, the value of \[m=\pm 7\sqrt{2}\].

Note:
Students make mistakes while adding, subtracting or dividing the correct numbers to simplify the given equation. we should always remember to write the plus or minus symbol whenever we take roots. We should also know to simplify the terms inside the root.