Question

How do you solve $2{{x}^{2}}-25x=0$ ?

Answer 1

Hint: In this question, we have to find the value of x. The equation is in the form of a quadratic, therefore, we will apply the discriminant method to solve this problem. We will first compare the given equation with the general form of quadratic equation to get the value of a, b, and c. Then, we will find the value of discriminant $D=\sqrt{{{b}^{2}}-4ac}$, and thus apply the discriminant formula $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . After the necessary calculations, we get two equations , so we solve them separately to get the value of x, which is our required answer.

Complete step by step solution:
According to the question, a quadratic equation is given to us and we have to solve the equation for the value of x.
The equation is $2{{x}^{2}}-25x=0$ ----------------- (1)
As we know, the general quadratic equation is in form of $a{{x}^{2}}+bx+c=0$ ---------- (2)
Thus, on comparing equation (1) and (2), we get $a=2,$ $b=-25,$ and $c=0$ ------- (3)
So, now we will apply the discriminant formula $D=\sqrt{{{b}^{2}}-4ac}$ by putting the above values in the formula, we get
$\begin{align}
  & \Rightarrow D=\sqrt{{{(-25)}^{2}}-4.(2).(0)} \\
 & \Rightarrow D=\sqrt{625} \\
\end{align}$
Thus, on further solving, we get
$\Rightarrow D=25$ -------------- (4)
We see that the square root has a positive term which implies the discriminant has real roots.
Now, we will apply the discriminant formula, which is
$\Rightarrow x=\dfrac{-b\pm D}{2a}$
$\Rightarrow x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ --------------- (5)
So, we will put the value of equation (3) and (4) in equation (5), we get
$\Rightarrow x=\dfrac{-(-25)\pm 25}{2.(2)}$
On further simplification, we get
$\Rightarrow x=\dfrac{25\pm 25}{4}$
Therefore, we will split the above equation in terms of (+) and (-) sign, we get
$\Rightarrow x=\dfrac{25+25}{4}$ -------- (6) , or
 $\Rightarrow x=\dfrac{25-25}{4}$ ---------- (7)
Now, we will first solve equation (6), we get
$\Rightarrow x=\dfrac{50}{4}$
Thus, on further simplification, we get
$\Rightarrow x=\dfrac{25}{2}$
 Now, we will first solve equation (7), we get
$\Rightarrow x=\dfrac{0}{4}$
Thus, on further simplification, we get
$\Rightarrow x=0$

Therefore, for the equation $2{{x}^{2}}-25x=0$ , we get the value of $x=\dfrac{25}{2},0$.

Note: While solving this problem, do step-by-step calculations to avoid mathematical errors. You can also use the cross multiplication method to get the required solution to the problem. One of the alternative methods to solve the problem is take x common from the given equation, and thus solve the equations separately to get an accurate answer.