👉 To explain the math behind a problem, we start by identifying the key concepts and operations involved. For instance, if we're dealing with linear equations like \(2x + 3 = 7\), we first isolate the variable \(x\) by subtracting 3 from both sides (\(2x = 4\)), then divide by 2 (\(x = 2\)). For quadratic equations, like \(x^2 + 5x + 6 = 0\), we apply the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 1\), \(b = 5\), and \(c = 6\). This formula calculates the roots by solving the discriminant (\(b^2 - 4ac\)) and then substituting back into the formula. For exponential or logarithmic problems, we use properties like \(a^b = e^{b\ln(a)}\) or \(\log_a(b) = \frac{\ln(b)}{\ln(a)}\), simplifying complex expressions into more manageable forms. Understanding these basic operations and formulas is crucial for tackling a wide range of mathematical problems efficiently.
