SOLUTION: What is the solution of this equation? 1+sqrt(3x+3)=sqrt(7x+2)

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Question 1021311: What is the solution of this equation?
1+sqrt(3x+3)=sqrt(7x+2)
Found 3 solutions by josgarithmetic, addingup, MathTherapy:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Need to square twice. Much algebra steps.

1%2B2sqrt%283x%2B3%29%2B3x%2B3=7x%2B2

2sqrt%283x%2B3%29=7x%2B2-1-3x-3

2sqrt%283x%2B3%29=4x-2

sqrt%283x%2B3%29=2x-1

3x%2B3=4x%5E2-4x%2B1

4x%5E2-7x-2=0

x=%287%2B-+sqrt%2849-4%2A4%2A%28-2%29%29%29%2F%282%2A4%29

x=%287%2B-+sqrt%2881%29%29%2F8

x=%287%2B-+9%29%2F8
either x=-1/4 or x=2
and you might need to check if the MINUS form will work.




(Solution was corrected.)

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
1+sqrt(3x+3) = sqrt(7x+2)
Raise both sides to the power of 2:
(1+sqrt(3 x+3))^2 = 7x+2
Subtract 7x+2 from both sides:
-2-7x+(1+sqrt(3x+3))^2 = 0
-2-7x+(1+sqrt(3x+3))^2
= 2-4x+2sqrt(3x+3) = 0
Simplify and substitute y = sqrt(3 x+3):
2-4x+2sqrt(3x+3) = 6+2 sqrt(3x+3)-(4 sqrt(3x+3)^2)/(3)
= -(4 y^2)/3+2 y+6 = 0:
-(4 y^2)/3+2 y+6 = 0
The left hand side factors into a product with four terms:
-2/3 (y-3) (2 y+3) = 0
Multiply both sides by -3/2:
(y-3) (2 y+3) = 0
Split into two equations:
y-3 = 0 or 2 y+3 = 0
Add 3 to both sides:
y = 3 or 2 y+3 = 0
Substitute back for y = sqrt(3 x+3):
sqrt(3 x+3) = 3 or 2 y+3 = 0
Raise both sides to the power of two:
3 x+3 = 9 or 2 y+3 = 0
Subtract 3 from both sides:
3 x = 6 or 2 y+3 = 0
Divide both sides by 3:
x = 2 or 2 y+3 = 0
Subtract 3 from both sides:
x = 2 or 2 y = -3
Divide both sides by 2:
x = 2 or y = -3/2
Substitute back for y = sqrt(3 x+3):
x = 2 or sqrt(3 x+3) = -3/2
Raise both sides to the power of two:
x = 2 or 3 x+3 = 9/4
Subtract 3 from both sides:
x = 2 or 3 x = -3/4
Divide both sides by 3:
x = 2 or x = -1/4
1+sqrt(3 x+3) => 1+sqrt(3+(3 (-1))/4) = 5/2
sqrt(7 x+2) => sqrt(2+(7 (-1))/4) = 1/2:
So this solution is incorrect
1+sqrt(3 x+3) => 1+sqrt(3+3 2) = 4
sqrt(7 x+2) => sqrt(2+7 2) = 4:
So this solution is correct
The solution is:
Answer: |
| x = 2

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

What is the solution of this equation?
1+sqrt(3x+3)=sqrt(7x+2)
1+%2B+sqrt%283x+%2B+3%29+=+sqrt%287x+%2B+2%29

1+%2B+2sqrt%283x+%2B+3%29+%2B+3x+%2B+3+=+7x+%2B+2 ------ Squaring both sides

4+%2B+3x+%2B+2sqrt%283x+%2B+3%29+=+7x+%2B+2

2sqrt%283x+%2B+3%29+=+7x+%2B+2+-+4+-+3x

2sqrt%283x+%2B+3%29+=+4x+-+2

2sqrt%283x+%2B+3%29+=+2%282x+-+1%29

sqrt%283x+%2B+3%29+=+2%282x+-+1%29%2F2

sqrt%283x+%2B+3%29+=+2x+-+1

3x+%2B+3+=+4x%5E2+-+4x+%2B+1 ------ Squaring both sides

0+=+4x%5E2+-+4x+%2B+1+-+3x+-+3

0+=+4x%5E2+-+7x+-+2

0 = (x - 2)(4x + 1) 

highlight_green%28x+=+2%29        OR          x+=+-+1%2F4 (ignore as this is an EXTRANEOUS SOLUTION