Question

PLEASE Help!! What is the solution of the equation? Eliminate any extraneous solutions.

Answer 1

D. -4

sq rt of 3x+28-8=x
add 8 to both sides

sq rt of 3x+28 = x+8
square both sides of the equation

3x + 28 = x^2 + 16x + 64

subtract x^2+16x+64 from both sides
group common terms
-13x-36-x^2=0

rearrange and put in quadratic form

x= -13 +/- sq rt of 13^2-4(1)(36) over 2(1)

subtract 169 by 144

x= -12 +/- sq rt of 25 over 2

solve for both sides

x = -13+5 over 2
=-4

x= -13-5 over 2
= -9

now plug in x

sq rt of 3(-4)+28   -8=-4
sq rt of 3(-9)+28    -8= -9

-4 = -4
but
-7 does not = -9

so -4 is the solution