Question

Solve the quadratic equation 2x2+ax-a2=0 for x

Answer 1

$\bold{x=\frac{a}{2},-a}$ is the value of the quadratic equation $\bold{2 x^{2}+a x-a^{2}=0.}$

Given:

$2 x^{2}+a x-a^{2}=0$

To find:

Value of x=?

Solution:

To solve the equation $2 x^{2}+a x-a^{2}=0$, we have to first find the value of the “a” in the equation $2 x^{2}+a x-a^{2}=0$

We will use the separation method that is finding the common factor we get

$2 x^{2}+a x-a^{2}=0$

$2 x^{2}+2 a x-a x-a^{2}=0$

Now subtracting $ax$ from $2ax$ we get  

$\begin{array}{l}{2 x(x+a)-a(x+a)=0} \\ {2 x-a, x+a}\end{array}$

After solving the quadratic equation for the value of “a” we get the value of: “x” as $x=\frac{a}{2},-a$

Therefore, the value of the quadratic equation after solving is $\bold{x=\frac{a}{2},-a}$

Answer 2

Answer:

$x=-a\:Or \:x=\frac{a}{2}$

Step-by-step explanation:

$Given \: quadratic\: equation:\\2x^{2}+ax-a^{2}=0$

/* Splitting the middle term, we get

$2x^{2}+2ax-ax-a^{2}=0$

$\implies 2x(x+a)-a(x+a)=0$

$\implies (x+a)(2x-a)=0$

$\implies x+a=0\:Or \:2x-a=0$

$\implies x=-a\:Or \:2x=a$

$\implies x=-a\:Or \:x=\frac{a}{2}$

Therefore,

$x=-a\:Or \:x=\frac{a}{2}$

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