SOLUTION: Solve each equation for x.
2(x-5)^2 = 3
My anwer was:x={{{2sqrt(6+10)/2}}},x={{{2sqrt(-6+10)/2}}}. Is this correct? Thanks.
Algebra.Com
Question 75009This question is from textbook Beginning Algebra
: Solve each equation for x.
2(x-5)^2 = 3
My anwer was:x=,x=. Is this correct? Thanks.
This question is from textbook Beginning Algebra
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
.
You can solve this by first dividing both sides by 2. This removes the factor of 2 on the
left side. After the division by 2 the equation becomes:
.
.
Take the square root of both sides to get:
.
.
The right side of this equation generates both positive and negative answers. So we end up
with two answers for x-5. They are and .
.
Add +5 to both sides of both equations and you get:
.
and
.
One more thing. It is against convention to leave a radical in the denominator. So we need
to work on because that is equal to . We can rationalize
this fraction by multiplying it by which is the same as multiplying
it by 1, so it doesn't change the value of the fraction. This multiplication becomes:
.
.
The denominator is rationalized to become 2 and the numerator becomes
which becomes .
.
The result is and when this is substituted into the equations for x, the
result is:
.
and
.
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