How do I solve this?? sqrt x^2+3x+7 = x+2 ????

Answer 1

Hey there!

Here's the answer.

sqrt(x^2+3x+7)=x+2 --> Write the problem.
x^2+3x+7=x^2+4x+4 --> Square both sides of the equation.
3x+7=4x+4 --> Subtract x^2 on both sides of the equation.
-x+7=4 --> Subtract 4x on both sides of the equation.
-x=-3 --> Subtract 7 on both sides of the equation.
x=3 Divide -1 on both sides of the equation.

Check to see whether the solution is correct.

sqrt(3^2+3(3)+7)=3+2 -->
sqrt(9+9+7)=5 -->
sqrt(25)=5 -->
5=5, true

Since the solution satisfies the equation, the answer is x=5.

Hope it helps!

Answer 2

Whenever you have a n equation to be solved that involves a radical ( that's stuff under a square root sign), you should isolate the radical expression, then square both sides of the equation.
For your problem, I'm going to assume you meant
everything on the left side of the equation was under the square root sign, not just the x^2 term. In that case the radical term is already isolated.

Squaring both sides gives me x^2+3x+7=(x+2)^2
x^2+3x+7 = x^2+4x+4
x^2 -x^2 +3x-4x = 4-7
-x =-3, x=3
Verify! Sq.rt.[(3^2+3(3) +7] =(3+2)
sq rt.(9+9+7)= 5
sqrt25 =5
5=5

Actually sqrt25 = + or - 5, but you can ignore the -5 answer as one that mathematically does not satisfy the equality.

I hope this helps.

Answer 3

Square both sides

x^2 + 3x + 7 = (x + 2)^2

x^2 + 3x + 7 = x^2 + 4x + 4 // -x^2

3x + 7 = 4x + 4 // - 3x

7 = x + 4 // -4 , and change sides

x=3

Checking the solution:
x^2 + 3x + 7 = 3^2 + 3*3 + 7 = 9+9+7 = 25, which is valid for function sqrt
sqrt(25)=? x+2
5 =? 3 + 2
5 =? 5
Yes, 5=5

Answer 4

Start by squaring both sides:
x^2 + 3x + 7 = x^2 + 4x + 4
combine like terms: (cancel the x^2 and move the x terms)
0 = x - 3
x = 3

Check:
sqrt(25) = 5 = 3 + 2 Yep!

Answer 5

sqrt(x^2+3x+7)=x+2
take square of both sides;
x^2+3x+7=x^2+4x+4
x=3 ANS.

Answer 6

subtract the 3x and the 7 to get -2x-5 on the right side

now square the square root to get 4

4 = -2x-5
+5 +5
9/2 = -2x/2
4.5=-x
x =-4.5