Question 614338
Given to solve:
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{{{sqrt(x^2 - 9) =4}}}
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Square both sides to get:
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{{{x^2 - 9 = 16}}}
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add 9 to both sides to get rid of the -9 on the left side:
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{{{x^2 = 25}}}
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Take the square root of both sides to get the two answers:
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{{{x = 5}}} and {{{x = -5}}}
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You can check these two answers by returning to the original equation of:
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{{{sqrt(x^2 - 9) =4}}}
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and first substituting +5 for x to get:
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{{{sqrt(5^2 - 9) = 4}}}
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Square the 5 and this equation becomes:
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{{{ sqrt(25 - 9) = 4}}}
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Do the subtraction on the left side to get:
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{{{sqrt(16) = 4}}}
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4 is the square root of 16, so this equation reduces to:
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{{{4 = 4}}}
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And since this is true, we know that if x = +5, the equation works and therefore +5 is a solution.
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Next, return to the original equation of:
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{{{sqrt(x^2 - 9) =4}}}
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and this time substitute -5 for x to get:
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{{{sqrt((-5)^2 - 9) = 4}}}
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Square the -5  to again get +25 and this equation becomes:
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{{{ sqrt(25 - 9) = 4}}}
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Just like last time do the subtraction on the left side to get:
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{{{sqrt(16) = 4}}}
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Again, 4 is the square root of 16, so this equation reduces to:
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{{{4 = 4}}}
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And since this is true, we know that if x = -5, the equation works and therefore -5 is also a solution.
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Hope this helps you to understand the problem a little more and you can see how to solve and check a problem such as this one.
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