Question

How do you solve \[{x^2} = 78\]?

Answer 1

Hint: In the given question, we have been given an algebraic expression. It is a quadratic expression. It involves two terms – a variable raised to power of two and a constant. We have to solve the expression. To do that, we are first going to take the constant to the other side. Then we are going to express it in the form of a square and then solve it.

Formula Used:
We are going to use the formula of difference of two squares, which is:
\[{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)\]

Complete step-by-step answer:
In the given question, we are given the following expression:
\[{x^2} = 78\]
First, we take \[78\] to the other side,
$\Rightarrow$ \[{x^2} - 78 = 0\]
Now, we express \[78\] as a square,
$\Rightarrow$ \[{x^2} - {\left( {\sqrt {78} } \right)^2} = 0\]
Now, we apply the formula of difference of squares,
$\Rightarrow$ \[\left( {x - \sqrt {78} } \right)\left( {x + \sqrt {78} } \right) = 0\]
Now, \[x - \sqrt {78} = 0\] and \[x + \sqrt {78} = 0\]
Taking the constant to the other side in both the equations,
$\Rightarrow$ \[x = \sqrt {78} \] and \[x = - \sqrt {78} \]

Note: In the given question we had to solve an algebraic expression. To do that, we first brought all the terms on one side. Then we expressed the constant term in the form of a square as the variable was also a square. Then we applied the formula of difference of squares and solved the question.