math b question??

Question

1.find the solution set of equation RADICAL 9x+10 = x

2. Express in simples a=bi form the roots of equations xSQUARED+5=4x

3. FIND VALUE OF K . WILL THE ROOTS OF EQUATIONS 2Xsquared -4X+k be REAL AND EQUAL.

Answer 1

1.) √(9x + 10) = x
9x + 10 = x^2
x^2 - 9x - 10 = 0
x = 10, x = -1
Since we squared both sides we must check for extraneous roots:
√(9(10) + 10) = 10
√100 = 10
10 is a solution
√(9(-1) + 10) = -1
√1 = -1
While -1 is a square root of 1, when a radical appears in an equation it denotes the positive square root, so -1 is not a solution.
2.) x^2 - 4x + 5 = 0
x = (-b +/- √[b^2 - 4ac])/2a
x = (4 +/- √[16 - 4(5)]/2
x = (4 +/- √-4)/2
x = (4 +/- 2i)/2
x = 2 +/- i
3.) x^2 - 4x + k = 0
x^2 - 4x + 4 = 0
(x - 2)(x - 2) = 0
k = 4