How do you solve using the completing the square method $x^{2} = x$ $x^2=x$ ?

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How do you solve using the completing the square method $x^{2} = x$ $x^2=x$ ?

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Answer 1 · 2016-02-27T10:56:36

This would be a very roundabout way in this case.

Explanation:

$\to x^{2} - x = 0 \to x (x - 1) = 0 \to x = 0 or x = 1$ $->x^2-x=0->x(x-1)=0->x=0orx=1$

Completing the square (if you really must):
$x^{2} - x = 0$ $x^2-x=0$ , so the number with $x$ $x$ is $- 1$ $-1$
Take half of that and square it:
$x^{2} + 2 \cdot (- \frac{1}{2}) \cdot x + {(- \frac{1}{2})}^{2} = {(x - \frac{1}{2})}^{2}$ $x^2+2*(-1/2)*x+(-1/2)^2=(x-1/2)^2$ , is the square we look for.

We have to add the ${(- \frac{1}{2})}^{2}$ $(-1/2)^2$ also to other side.

So: ${(x - \frac{1}{2})}^{2} = {(- \frac{1}{2})}^{2}$ $(x-1/2)^2=(-1/2)^2$

$\to x - \frac{1}{2} = \pm \frac{1}{2} \to x = 0 or x = 1$ $->x-1/2=+-1/2->x=0orx=1$

I prefer the first way, to be honest, but if you have to use the other method, you can still use the first to check your answer.

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How do you solve using the completing the square method $x^{2} = x$ $x^2=x$ ?

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Explanation:

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How do you solve using the completing the square method x2=xx^2=x?

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How do you solve using the completing the square method $x^{2} = x$ $x^2=x$ ?