Can someone help me solve this please?

[SQRT(2x2 + 6x + 4)] = x + 1

Square both sides.

2x^2 + 6x + 4 = x^2 +2x + 1
x^2 + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = -3 or -1
The -3 solution assumes -2 is a valid square root of root 4. Some teachers may disagree.

2 x^2 + 6 x + 4 = x^2 + 2 x + 1

x^2 + 4 x + 3 = 0
(x+3)(x+1) = 0
x = -3 or x = -1 only one may work so check
x = -3
sqrt (18- 18+4) = -3+1
sqrt 4 = -2 ? well, not really
check
x = -1
sqrt (2 -6+4) = -1+1 = 0 yes

Square both sides:

2x^2 + 6x + 4 = (x+1)^2

We also have to demand that the argument of the square root is positive. So,

2x^2 + 6x + 4 >=0,

but any solution of the above quadratic equation will automatically satisfy this condition, because the right hand side is a perfect square (x+1)^2 which is always non-negative.

So, we have to solve the equation:

x^2 + 4 x + 3 = 0 -->

(x+1)(x+3) = 0 --->

x = -1, or x = -3

I like that Count Iblis :)

I forgot the condition that the square root itself must be positve as pointed out by Drwls and Damon. So, only x = -1 is a valid solution.

Note that you could define a different square root function that is always less or equal than zero, but in that case, you have only the x = -3 as the solution.

We discussed this the other day and decided that for working with square root functions we should hedge the subject to saying sqrt of anything is +, but the negative is perfectly reasonable.

Sure, I can help you solve this equation.

To solve the equation [SQRT(2x^2 + 6x + 4)] = x + 1, we need to follow these steps:

Step 1: Isolate the square root
First, we'll isolate the square root on one side of the equation. We do this by subtracting (x + 1) from both sides:
SQRT(2x^2 + 6x + 4) - (x + 1) = 0

Step 2: Square both sides
Next, we square both sides of the equation to eliminate the square root:
[SQRT(2x^2 + 6x + 4) - (x + 1)]^2 = 0^2

Step 3: Simplify the expression
When we expand and simplify the squared expression, we get:
2x^2 + 6x + 4 - 2(x + 1) SQRT(2x^2 + 6x + 4) + (x + 1)^2 = 0

Step 4: Simplify further
Now, we simplify the expression:
2x^2 + 6x + 4 - 2x - 2 SQRT(2x^2 + 6x + 4) + x^2 + 2x + 1 = 0

Combining like terms, we have:
3x^2 + 6x + 5 - 2 SQRT(2x^2 + 6x + 4) = 0

Step 5: Isolate the square root
Move the square root term to the other side of the equation:
3x^2 + 6x + 5 = 2 SQRT(2x^2 + 6x + 4)

Step 6: Square both sides again
Square both sides of the equation to eliminate the square root:
(3x^2 + 6x + 5)^2 = (2 SQRT(2x^2 + 6x + 4))^2

Step 7: Simplify the expression
Expanding and simplifying the squared expressions, we have:
9x^4 + 36x^3 + 71x^2 + 60x + 25 = 4(2x^2 + 6x + 4)

Step 8: Simplify further and rearrange the terms
Rearrange and simplify the equation:
9x^4 + 36x^3 + 71x^2 + 60x + 25 = 8x^2 + 24x + 16

Step 9: Combine like terms
Combine like terms on both sides of the equation:
9x^4 + 36x^3 + 63x^2 + 36x + 9 = 0

Step 10: Factor or use numerical methods
Now, you can try factoring this polynomial equation and solving for x. Alternatively, you can use numerical methods such as graphing or using a calculator to find the solutions.

I hope this explanation helps you solve the equation!