Question 498825: I don't understand how to solve this problem. Thank you.
It says solve and check the quadratic equation below by taking the square root of both sides. Express irrational answers in rational form.
(x-10)^2=4
thank you so much
Found 3 solutions by Theo, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equation is:
(x-10)^2=4
take the square root of both sides of the equation to get:
x-10 = sqrt(4) which becomes:
x-10 = 2
add 10 to both sides of the equation to get:
x = 12
substitute for x in the original equation to get:
(12-10)^2 = 4
simplify to get:
2^2 = 4
simplify further to get:
4 = 4
x = 12 is confirmed as good.
that's your answer.
Answer by ikleyn(52832)  (Show Source):
You can put this solution on YOUR website! .
Solve and check the quadratic equation below by taking the square root of both sides. Express irrational answers in rational form.
(x-10)^2=4
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In his post, tutor @Theo lost some solutions to given equations.
So, his treatment of the problem is incomplete.
I came to bring a correct complete solutions.
Your starting equation is
(x-10)^2 = 4. (1)
Take square root of both sides. You will get
x-10 = +/-2. <<<---=== square root of 4 has two values: 2 and -2.
It means that we have two cases.
Case 1. x-10 = 2. Then x = 2+10 = 12.
Case 2. x-10 = -2. Then x = -2+10 = 8.
So, equation (1) has two solutions. They are x = 8 and x = 12.
Check. Substitute these values into equation (1) to make sure that they suit perfectly.
Solved correctly.
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It might seem the loss of roots is a minor issue.
In fact, it is not so.
Loss of roots is a failed test of understanding square roots.
So, solving this equation correctly or incorrectly is an easy way
to check if a person does understand the subject.
In 10 seconds, everything becomes clear.
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Notice that the problem's formulation is like a lame horse with three legs.
Indeed, it says " Express irrational answers in rational form. "
Firstly, it is IMPOSSIBLE to do.
Secondly, it shows that a person, who wrote it, is mathematically illiterate.
Answer by josgarithmetic(39623)  (Show Source):
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