SOLUTION: 15. Solve the equation. Identify any extraneous solutions. x= sqrt-7x+8 A. 8 is a solution to the original equation. The value –1 is an extraneous solution. B.1 and

Algebra ->  Square-cubic-other-roots -> SOLUTION: 15. Solve the equation. Identify any extraneous solutions. x= sqrt-7x+8 A. 8 is a solution to the original equation. The value –1 is an extraneous solution. B.1 and       Log On


   

Question 397364: 15. Solve the equation. Identify any extraneous solutions.
x= sqrt-7x+8


A. 8 is a solution to the original equation. The value –1 is an extraneous solution.
B.1 and –8 are solutions.
C.1 and 8 are both extraneous solutions.
D.1 is a solution to the original equation. The value –8 is an extraneous solution.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x=+sqrt%28-7x%2B8+%29....
x%5E2=+-7x%2B8
x%5E2+%2B+7x+-+8+=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B7%2Ax-8=0 ( notice a=1, b=7, and c=-8)





x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=7, and c=-8




x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square 7 to get 49




x+=+%28-7+%2B-+sqrt%28+49%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32




x+=+%28-7+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-7+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-7+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-7+%2B+9%29%2F2 or x+=+%28-7+-+9%29%2F2


Lets look at the first part:


x=%28-7+%2B+9%29%2F2


x=2%2F2 Add the terms in the numerator

x=1 Divide


So one answer is

x=1




Now lets look at the second part:


x=%28-7+-+9%29%2F2


x=-16%2F2 Subtract the terms in the numerator

x=-8 Divide


So another answer is

x=-8


So our solutions are:

x=1 or x=-8




B. 1 and –8 are solutions