How do you solve $x^{2} - 6 x = 391$ $x^2 - 6x = 391$ by completing the square?

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How do you solve $x^{2} - 6 x = 391$ $x^2 - 6x = 391$ by completing the square?

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Answer 1 · 2016-04-12T07:29:39

$x = 23$ $x=23$ or $x - 17$ $x-17$

Explanation:

In $x^{2} - 6 x = 391$ $x^2-6x=391$ as the Left Hand Side is $x^{2} - 6 x$ $x^2-6x$ , we can make it a complete square (compare it with ${(x - a)}^{2} = x^{2} - 2 a x + a^{2}$ $(x-a)^2=x^2-2ax+a^2$ ) by adding **square of half the coefficient of $x$ $x$ .

As coefficient of $x$ $x$ is $- 6$ $-6$ , we need to add ${(- \frac{6}{2})}^{2} = 9$ $(-6/2)^2=9$ , to each side and then we have

$x^{2} - 6 x + 9 = 391 + 9 = 400$ $x^2-6x+9=391+9=400$

or ${(x - 3)}^{2} = 20^{2}$ $(x-3)^2=20^2$

Hence either $x - 3 = 20$ $x-3=20$ or $x - 3 = - 20$ $x-3=-20$ i.e.

$x = 23$ $x=23$ or $x - 17$ $x-17$

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How do you solve $x^{2} - 6 x = 391$ $x^2 - 6x = 391$ by completing the square?

1 Answer

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Science

Math

Humanities

... and beyond

How do you solve x2−6x=391x^2 - 6x = 391 by completing the square?

1 Answer

Explanation:

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Impact of this question

How do you solve $x^{2} - 6 x = 391$ $x^2 - 6x = 391$ by completing the square?