SOLUTION: whats the answer and how do you do thia problem dealing with Sums of Radicals; Binomials and Equations Containing Radical: The square root of (d^2-19)minus 2d plus 11 equal 0

Question 20533: whats the answer and how do you do thia problem dealing with Sums of Radicals; Binomials and Equations Containing Radical:
The square root of (d^2-19)minus 2d plus 11 equal 0
Answer by mmm4444bot(95) (Show Source): You can put this solution on YOUR website!
Hello There:
Solving an equation that contains one radical term requires that you first isolate the radical on one side of the equals sign and then square both sides.
sqrt(d^2 - 19) - 2*d + 11 = 0
Add 2*d and subtract 11 from both sides to isolate the radical.
sqrt(d^2 - 19) = 2*d - 11
Next, square both sides.
d^2 - 19 = 4*d^2 - 44*d + 121
This is a quadratic equation. Let's put it into general form.
3*d^2 - 44*d + 140 = 0
Hopefully, you know how to solve this using the quadratic formula.
Do this gives us two candidates for the solution:
d = 14/3 and d = 10
NOTE: It is VERY IMPORTANT TO CHECK YOUR ANSWERS anytime you square both sides of an equation in the process of solving it. Squaring both sides can introduce solutions to the quadratic equation which do not work in the original equation.
Checking with the original equation, we find that 14/3 is not a solution.
Therefore, the answer is d = 10.
~ Mark

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