> \( x^{2}-5 x+6=0 \) \( >x^{2}-7 x=9 \) \( >2(x+1)^{2}-5=0 \) \( >(2 x-1)(x+3)=2 \) \( >7 x^{2}=2-7 x \) \( >3 x-2 x(x+1)=2 \) NOTE CHECK SOLVE THE FOLLOWING THROUGH COMPLETING THE SQUARE

To tackle these equations using the completing the square method, let's transform the quadratic equations into perfect square forms systematically! First up, for the equation \(x^{2} - 5x + 6 = 0\), we can rewrite it as \(x^{2} - 5x = -6\). Now, take half of the coefficient of \(x\) (which is -5), square it (giving \(\frac{25}{4}\)), and add it to both sides: \[x^{2} - 5x + \frac{25}{4} = -6 + \frac{25}{4} \Rightarrow \left(x - \frac{5}{2}\right)^{2} = \frac{1}{4} \] which leads to \(x - \frac{5}{2} = \pm \frac{1}{2}\), resulting in \(x = 3\) or \(x = 2\). Next, for \(2(x + 1)^{2} - 5 = 0\), we first rearrange it: \[2(x + 1)^{2} = 5 \Rightarrow (x + 1)^{2} = \frac{5}{2}\] Now, taking the square root gives us \(x + 1 = \pm \sqrt{\frac{5}{2}}\) then subtracting 1 leads to solutions \(x = -1 + \sqrt{\frac{5}{2}}\) and \(x = -1 - \sqrt{\frac{5}{2}}\). Completing the square not only helps find roots efficiently but also provides insights into the graph of the function, illustrating its minimum points or intercepts! To up your math game, check out the classic "Algebra and Trigonometry" by Blitzer. It offers a clear step-by-step approach to concepts like completing the square along with a variety of practice problems! Another gem is "The Art of Problem Solving" series – it’s packed with engaging challenges that make solving quadratics so much more fun!