Solve for X: Finding the Value in (x+3)² = x² + 15

Let's solve the equation, first we'll simplify the algebraic expressions using the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$We will then apply the mentioned formula and expand the parentheses in the expression in the equation:

$(x+3)^2=x^2+15 \\ x^2+2\cdot x\cdot3+3^2=x^2+15\\ x^2+6x+9=x^2+15$We'll continue and combine like terms, by moving terms between sides. Then we can notice that the squared term cancels out, therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2+6x+9=x^2+15 \\ 6x=6\hspace{8pt}\text{/}:6\\ \boxed{x=1}$Therefore, the correct answer is answer B.