Question

How do you solve $2{x^2} + 10x = 0$?

Answer 1

Hint: Here we need to find the value of $x$ from the equation which is given as $2{x^2} + 10x = 0$.
As here the power of $x$ is $2$ and therefore we will get the two values of $x$ and therefore we can here we can take $2x$ common from the terms given and then we will get $2x\left( {x + 5} \right) = 0$ and then we can solve it to get the result.

Complete step by step solution:
Here we are given the equation in which we are given $2{x^2} + 10x = 0$
Here we need to solve this equation which means that we need to find the value of the unknown variable in the given equation which is $x$
As here the power of $x$ is $2$ and therefore we will get the two values of $x$
Now we can see that in the above given equation, we can take the variable $2x$ common from both the terms $2{x^2}{\text{ and }}10x$
So after taking $2x$ common we will get:
$2{x^2} + 10x = 0$
$2x\left( {x + 5} \right) = 0$$ - - - - \left( 1 \right)$
Now we must know that when we simplify the quadratic equation in the form of $\left( {x + a} \right)\left( {x + b} \right) = 0$ then we can write it separately as $x + a = 0{\text{ or }}x + b = 0$
Here we can write the equation (1) as:
\[2x = 0{\text{ or }}\left( {x + 5} \right) = 0\]
Hence we can solve them and we will get that:
$
  2x = 0 \\
  x = 0 \\
 $
And also we can write that:
$
  x + 5 = 0 \\
  x = - 5 \\
 $

Therefore we get the two values of $x$ as $0, - 5$

Note:
Here we must know that whenever we are given any quadratic equation of the form $a{x^2} + bx + c = 0$ and $c = 0$ then we can write $a{x^2} + bx = 0$ and $x = 0{\text{ or }}x = - \dfrac{b}{a}$.