Answer :
To solve the equation \((x+2)^2 + 8 = 15\), you need to follow these steps:
1. Expand the squared term:
\((x+2)^2 = x^2 + 4x + 4\)
2. Substitute the expansion back into the equation:
\(x^2 + 4x + 4 + 8 = 15\)
3. Combine like terms:
\(x^2 + 4x + 12 = 15\)
4. Rearrange the equation to set it equal to zero:
\(x^2 + 4x + 12 - 15 = 0\)
\(x^2 + 4x - 3 = 0\)
5. To solve this quadratic equation, you can use the quadratic formula:
\(x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}\)
In this case, \(a = 1\), \(b = 4\), and \(c = -3\).
6. Plug in the values and solve for \(x\):
\(x = \frac{-4 ± \sqrt{4^2 - 4*1*(-3)}}{2*1}\)
\(x = \frac{-4 ± \sqrt{16 + 12}}{2}\)
\(x = \frac{-4 ± \sqrt{28}}{2}\)
\(x = \frac{-4 ± 2√7}{2}\)
\(x = -2 ± √7\)
Therefore, the solution to the equation \((x+2)^2 + 8 = 15\) is \(x = -2 ± √7\), which matches option B.
