Question

How do you factor the expression \[4{x^2} - 49\] ?

Answer 1

Hint: Here given is an expression that is quadratic form but we will solve it by taking the square root on both sides since both the terms are perfect squares. We can easily take the roots of both the sides. After taking the roots we will assign it to two values of the root on RHS because a square of positive as well as negative number is al

Complete step-by-step answer:
Given that
\[4{x^2} - 49\]
Equating it to zero we get,
\[4{x^2} - 49 = 0\]
Now taking 49 on other side,
\[4{x^2} = 49\]
We can write the LHS as,
\[{\left( {2x} \right)^2} = 49\]
Now taking square root on both sides,
\[\left( {2x} \right) = \pm 7\]
Now we will equate the values one by one,
\[2x = 7 \] or \[2x = - 7\]
\[x = \dfrac{7}{2}\] or \[x = - \dfrac{7}{2}\]
This is our answer that is the factor of the given equation or expression.
So, the correct answer is “ \[x = \dfrac{7}{2}\] or \[x = - \dfrac{7}{2}\] ”.

Note: Here note that we can also solve this equation by quadratic formula or factorization method but that would take a little more time so we chose this method. Also note that when we take root on both sides it is necessary to take both the values of the RHS number that is positive as well as negative.
It is possible to take this way of solution since both sides are a perfect square. \[4{x^2}\] can be written as \[{\left( {2x} \right)^2}\] .