SOLUTION: Could you please help? Solve the following equations. Leave radicals in radical form ( do not calculate their approximate values.) a. {{{sqrt x+6-4=x}}} b. {{{(5)sqrt(3x+1)

Question 61078: Could you please help?
Solve the following equations. Leave radicals in radical form ( do not calculate their approximate values.)
a.
b. (the 5's should be at the tip of the radical sign)
c. (x+6)^2/5+2=3
Thank you for your help!!
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
(a) sqrt(x+6) - 4 = x
Addinfg 4 to either side we get,
sqrt (x+6) - 4 + 4 = x + 4
==> sqrt(x + 6) = x + 4
Squaring both the sides we have,
x + 6 = (x + 4)^2
==> x + 6 = x^2 + 8x + 16 [(a+b)^2 = a^2 + 2ab + b^2]
==> x = x^2 + 8x + 16 - 6
==> x = x^2 + 8x + 10
==> 0 = x^2 + 8x + 10 - x [adding -x to both the sides]
==> 0 = x^2 + 7x + 10
==> 0 = x^2 + 5x + 2x + 10 [Splitting the middle term]
==> 0 = x(x+5) + 2(x+5) [Taking out the common factor]
==> 0 = (x+5)(x+2)
==> x + 5 = 0 or x+2 = 0
==> x = -5 or x = -2

(b) (5)sqrt(3x+1)=(5)sqrt(x^2-2x-5)
Dividing both the sides by 5 we get,
sqrt(3x+1)= sqrt(x^2-2x-5)
Squaring both the sides,
3x + 1 = x^2 - 2x - 5
==> 3x + 1 - 3x = x^2 - 2x - 5 - 3x [ adding - 3x to both the sides]
==> 1 = x^2 - 5x - 5
==> 0 = x^2 - 5x - 5 - 1 [adding -1 to both the sides]
==> 0 = x^2 - 5x - 6
==> 0 = x^2 - 6x + x - 6
==> 0 = x(x-6) + 1(x-6)
==> 0 = (x-6)(x+1)
==> x - 6 = 0 or x + 1 = 0
==> x = 6 or x = -1
(c)[(x+6)^2]/5 + 2 = 3
==> (x+6)^2 /5 = 3-2 [Adding -2 to both the sides]
==> (x+6)^2/5 = 1
Multiplying both the sides by 5 we have,
(x+6)^2 = 1*5
==> (x+6)^2 = 5
==> x^2 + 12x + 36 = 5
==> x^2 + 12x + 36 - 5 = 0 [add -5 to both the sides]
==> x^2 + 12x + 31 = 0
This equation does not have exact values for x.
Please check the equation.

Good Luck!!!

RELATED QUESTIONS
Could someone help me? Solve the following equations. Leave radicals in radical... (answered by funmath)

Solve the following equation for x. [Do not report answers in decimal � leave them in... (answered by 303795)

Solve the following equation for x. [Do not report answers in decimal � leave them in... (answered by ankor@dixie-net.com)

Can you please help me solve and leave in simplest radical form the following: (((x^2+8x= (answered by josmiceli)

How do you solve equations like these? Rules:Simplify but leave in radical form 1.)... (answered by scott8148)

Solve the following equation for x. Hint: Factor the left hand side. [Do not report... (answered by brandonpark2889)

can you please help me use the quadratic formula to solve the following and leave... (answered by Mathtut)