Question

How do you solve \[6{x^2} = 1296\]?

Answer 1

Hint: Here in this question, we have to solve the given equation, the given equation is in the form of a quadratic equation. This is a quadratic equation for the variable x. By using the formula \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\], we can determine the solutions.

Complete step-by-step solution:
The question involves the quadratic equation. To the quadratic equation we can find the roots by factoring or by using the formula \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]. consider the given equation \[6{x^2} = 1296\]
Divide the above equation by 6 we get
. \[ \Rightarrow {x^2} = 216\]
Take 216 to the LHS and it is written as
\[ \Rightarrow {x^2} - 216 = 0\]
In general, the quadratic equation is represented as \[a{x^2} + bx + c = 0\], when we compare the above equation to the general form of equation the values are as follows. a=1 b=0 and c=216. Now substituting these values to the formula for obtaining the roots we have
\[x = \dfrac{{ - (0) \pm \sqrt {{{(0)}^2} - 4(1)( - 216)} }}{{2(1)}}\]
On simplifying the terms, we have
\[ \Rightarrow x = \dfrac{{0 \pm \sqrt {0 + 864} }}{2}\]
Now add 0 to 864 we get
\[ \Rightarrow x = \dfrac{{0 \pm \sqrt {864} }}{2}\]
The number 864 is not a perfect square number and we don’t have a square root for this. So, the square root is carried out as it is and so we have.
Therefore, we have \[x = \dfrac{{0 + \sqrt {864} }}{2}\] or \[x = \dfrac{{0 - \sqrt {864} }}{2}\]. We can simplify for further so we get
\[ \Rightarrow x = 14.697\] and \[x = - 14.697\]
hence we have solved the quadratic equation and found the value of the variable x.
The equation is also solved by using the factorisation method.

Note: The quadratic equation can be solved by using the factorisation method and we also find the roots by using the formula \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]. While factorising we use sum product rule, the sum product rule is given as the product factors of the number c is equal to the sum of the factors which satisfies the value of b.