To rewrite the equation by completing the square for \(2x^2 - 16x + 63 = 0\), follow these steps:
1. Begin with the equation in the form \(ax^2 + bx + c = 0\).
2. Divide the entire equation by the coefficient of the \(x^2\) term (in this case, 2) to have \(x^2 - 8x + \frac{63}{2} = 0\).
3. To complete the square, take half of the coefficient of the \(x\) term, square it, and add/subtract it to both sides of the equation. Half of -8 is -4, and \((-4)^2 = 16\), so add \(16\) to both sides:
\(x^2 - 8x + 16 + \frac{63}{2} = 16\)
4. Simplify the equation to get \((x - 4)^2 = \frac{13}{2}\).
Therefore, \((x - 4)^2 = \frac{13}{2}\) is the rewritten equation after completing the square for \(2x^2 - 16x + 63 = 0\).
