Algebra question. Solve and check the following equation.?

i would do:
y-4=s.r. of 2y+7
then square both sides
2y+7=y^2-8y+16
y^2-10y+9=0
factor.
(y-9)(y-1)
y=1,9

check: plug in the numbers.
[s.r of 2(1)+7]+4=1
7=1
does not work.
try the 9.
[s.r. of 2(9)+7]+4=9
5+4=9
9=9

y=9

Subtract 4 from both sides.

sqrt(2y + 7) = y - 4. Square both sides.
2y + 7 = y^2 - 8y + 16. Make it equal 0.
y^2 - 10y + 9 = 0.
(y - 9)(y - 1) = 0.
y = 9, y = 1

y = 1 doesn't work, though.
So the answer is y = 9.

Get the square root all by itself on one side of the equation. Then square both sides. This will get rid of the square root. Then simplify.

You sould eventually end up with something in the form of
ay^2 + by + c = 0, which you can then solve by factoring, completing the square, or the quadratic formula.

Somebody else said to just square both sides and claimed that this gives you 2y+7+16=y. This is wrong. First of all, you'd have y^2 on the other side if you were squaring both sides. Second of all, (a + b)^2 is NOT necessarily equal to a^2 + b^2. You just can't distribute the exponent like that. It doesn't work. You have to use the distributive rule or something like FOIL.

SQRT (2y+7) + 4 = y
SQRT (2y+7) = y - 4 Sub 4 fm each side of equation.
2y + 7 = (y-4)^2 Square each side.
2y + 7 = y^2-8y+16 Expand rt side.
2y = y^2 -8y+9 Sub 7 from each side.
0 = y^2-10y+9 Sub 2y from each side.
0= (y-9)(y-1) Factor the rt. side.
y-9=0, y=9 Set each factor = 0 and solve.
y-1=0, y=1

First you should try to get the variable together or make it less complicated. And oh, next time mention in your question what the question is, since you didn't directly say it.


√(2y + 7) + 4 = y ............. subtract 4 from both sides

√(2y + 7) = y - 4 .............. now square both sides

2y + 7 = (y - 4)^2 ............ square (y - 4)

2y + 7 = y^2 - 8y + 16 .... combine like terms

y^2 - 10y + 9 = 0 ............. factor to solve for y

(y - 9)(y - 1) = 0 ................ solve for y

y = 9 .. y = 1

there you go! you can plug it in and check if you want, but that should be it.

(sq root of 2y+7) = y-4
2y+7 = ( y-4) ^2
2y+7 = y^2 - 8y +16
y^2 -10y+9 = 0

(y-9)(y-1) = 0
y= 9 or 1

√2y+7+4=y
(√2y+7)² = (y-4)²
2y+7 = y²-8y+16
y²-8y-2y+16-7=0
y²-10y+9=0
(y-9)(y-1) = 0
y-9 = 0
y = 9

y-1 = 0
y=1

y = sqrt(2y + 7) + 4

Subtract 4 from both sides

y - 4 = sqrt(2y + 7)

Square both sides

y^2 - 8y + 16 = 2y + 7

Simplify

y^2 - 10y + 9 = 0

Solve for y

y = (10 +/- sqrt( 100 - 36) ) / 2

y = (10 +/- 8) / 2

y = 9 or 1

Check

2 * 9 + 7 = 25
sqrt(25) = +/- 5
+5 + 4 = 9

2 * 1 + 7 = 9
sqrt(9) = +/- 3
-3 + 4 = 1

√(2y + 7) + 4 = y

Bring 4 to the RHS.

√(2y + 7) = y - 4

Get rid of the (√) sign.

(2y + 7) = (y - 4)^2

Expand out the brackets.

(2y + 7) = (y^2 - 8y + 16)

Join all the variables and numbers together at one side and make it equal to 0 so as to solve the equation.

y^2 - 8y - 2y + 16 - 7 = 0

y^2 - 10y + 9 = 0

Factor out.

(y - 9) (y - 1) = 0

y = 9 or y = 1

isolate square root: sqrt(2y+7)=y-4
square both sides: (2y+7) = (y-4)^2
simplify: 2y+7=y^2-8y+16
simplify more: y^2-10y+9
factor: (y-9)(y-1)
y=1,9

sqrt(2y + 7) + 4 = y
sqrt(2y+7) = y-4


square both sides

2y+7 = y^2 - 8y +16
y^2 - 10y + 9 = 0

(y - 1)(y - 9) = 0

y = 1
and y = 9

square root of 2y+7) +4=y

square the: square root of 2y+7) and the 4

you get

2y+7+16=y
-2y
23= -y
divide by -1

y= -23


and i checked it its correct


plug it in if you want to I'm sure its right