Question

2(x+1)^2-(x-3)(x+3)=7+x^2

Answer 1

2x+4x+2-x²+9-7-x²=0

6x+4=0

3x+2=0

x= -2/3

Answer 2

Let's solve the given equation step by step:

2(x+1)^2 - (x-3)(x+3) = 7 + x^2

First, let's simplify the equation by expanding the square and multiplying the binomials:

2(x^2 + 2x + 1) - (x^2 - 9) = 7 + x^2

Next, distribute the 2 to the terms inside the parentheses:

2x^2 + 4x + 2 - (x^2 - 9) = 7 + x^2

Remove the parentheses:

2x^2 + 4x + 2 - x^2 + 9 = 7 + x^2

Combine like terms on both sides:

x^2 + 4x + 11 = 7 + x^2

The x^2 terms on both sides cancel out:

4x + 11 = 7

Subtract 11 from both sides:

4x = 7 - 11

4x = -4

Divide by 4:

x = -4/4

Simplifying the right side:

x = -1

So the solution to the equation is x = -1.