How do you solve the equation ${(x - 12)}^{2} = 121$ $(x-12)^2 = 121$ using the square root property?

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How do you solve the equation ${(x - 12)}^{2} = 121$ $(x-12)^2 = 121$ using the square root property?

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Answer 1 · 2015-08-13T15:33:06

The solutions are
$x = 1, x = 23$ $color(blue)(x=1, x=23$

Explanation:

The square root property involves taking the square root of both the terms on either side of the equation.

Applying the same to the given equation:

$\sqrt{{(x - 12)}^{2}} = \sqrt{121}$ $sqrt((x-12)^2)=sqrt(121$

( $\sqrt{121} = \pm 11$ $sqrt121= color(blue)(+-11$ )

So,
$\sqrt{{(x - 12)}^{2}} = \pm 11$ $sqrt((x-12)^2)=color(blue)(+-11$

$(x - 12) = \pm 11$ $(x-12)=color(blue)(+-11$

Solution 1:
$x - 12 = + 11$ $x-12 = +11$
Isolating $x$ $x$
$x - 12 + 12 = + 11 + 12$ $x-12 +color(blue)(12)= +11+color(blue)(12)$
$x = 23$ $color(blue)(x=23$

Solution 2:
$x - 12 = - 11$ $x-12 = -11$
Isolating $x$ $x$
$x - 12 + 12 = - 11 + 12$ $x-12 +color(blue)(12)= -11 +color(blue)(12)$
$x = 1$ $color(blue)(x=1$

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How do you solve the equation ${(x - 12)}^{2} = 121$ $(x-12)^2 = 121$ using the square root property?

1 Answer

Explanation:

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How do you solve the equation (x−12)2=121(x-12)^2 = 121 using the square root property?

1 Answer

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How do you solve the equation ${(x - 12)}^{2} = 121$ $(x-12)^2 = 121$ using the square root property?