Question

How do you solve \[5{x^2} - 90 = 0\] ?

Answer 1

Hint:Factoring reduces the higher degree equation into its reduced equation. In the above given equation, we need to reduce the quadratic equation either solving this by factorization or using algebraic identity where the square of addition of terms will give the factors from the equation.

Complete step by step answer:
The above equation is a quadratic equation which includes at least one monomial which has the greatest power of 2. But we have only two terms one with power of 2 and other with power of 0, the third term is not present. We can generate the third term by using the algebraic identity which is given as:
\[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]
So, we need to bring and convert the equation in the above form .First thing we need to do is get the terms a and b.
So, we will divide the above equation with 5 we will get,
\[{x^2} - 18 = 0\]
Now shifting the second term with power zero on the right-hand side we get the following equation,
\[{x^2} = 18\]
Now to find the value of variable x we need to take square root on both sides of the equation we get,
\[x = \pm \sqrt {18} \]
 On further solving the root we get,
\[\therefore x = \pm 3\sqrt 2 \]

Therefore, the value we get is \[x = \pm 3\sqrt 2 \].

Note:An important thing to note is that we can also solve this type of equation by using a perfect square method .But this method cannot be applied in this kind of equation because the second term 18 in the given equation is not a perfect square.