Question

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Answer 1

Answer:

Option C) ${\{0.5,0}\}$ is correct

The solution to the given equation is ${\{0.5,0}\}$

Step-by-step explanation:

Given quadratic equation is $-2x^2+x=0$

To solve the equation by completing the square :

$-2x^2+x=0$

$-2(x^2-\frac{x}{2})=0$

$x^2-\frac{x}{2}=0$

Rewritting the above equation as below :

$x^2-2(x)\frac{1}{4}+\frac{1}{4^2}-\frac{1}{4^2}=0$

$(x-\frac{1}{4})^2-\frac{1}{4^2}=0$

$(x-\frac{1}{4})^2=\frac{1}{4^2}$

Taking square root on both sides we get

$\sqrt{(x-\frac{1}{4})^2}=\sqrt{\frac{1}{4^2}}$

$(x-\frac{1}{4})=\pm\frac{1}{4}$

$x=\pm\frac{1}{4}+\frac{1}{4}$

$x=+\frac{1}{4}+\frac{1}{4}$ and $x=-\frac{1}{4}+\frac{1}{4}$

$x=\frac{2}{4}$ and $x=0$

Therefore $x=\frac{1}{2}$ and x=0

$x=0.5$ and x=0

Therefore the solution to the given equation is ${\{0.5,0}\}$

Option C) ${\{0.5,0}\}$ is correct