Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer. square root of the quantity x plus 7 end quantity minus 1 equals x

Step-by-step explanation:

If you call "5x-2x^2+1" an "equation," then you must equate 5x-2x^2+1 to 0:

5x-2x^2+1 = 0

This is a quadratic equation.  Rearranging the terms in descending order by powers of x, we get:

-2x^2 + 5x + 1 = 0.  Here the coefficients are a = -2, b = 5 and c = 1.

Use the quadratic formula to solve for x:

First find the discriminant, b^2 - 4ac:  25 - 4(-2)(1) = 25 + 8 = 33

Because the discriminant is positive, the roots of this quadratic are real and unequal.

                                                             -b ± √(discriminant)

Applying the quadratic formula   x =

                                                                         2a

we get:

      -5 ± √33           -5 + √33

x = = and

           2(-2)                     -4

                                  -5 - √33

                                         -4