SOLUTION: if a number is added to its square,the result is 42.find the number.
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if a number is added to its square,the result is 42.find the number.
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let number be
if a number (
) is added to its square (
),the result is
.....use quadratic formula
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve
Plug in a=1, b=1, and c=-42
Square 1 to get 1
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this
Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
Lets look at the first part:
Add the terms in the numerator
So one answer is
Now lets look at the second part:
Subtract the terms in the numerator
So another answer is
So our solutions are:
so, one answer is
and another answer is