To determine which of the given quadratic equations can be solved by factoring, we should first rewrite each equation in the standard form \(ax^2 + bx + c = 0\) and then check if they can be factored easily.
-
\(x^2 = 4x - 10\)
Rearranging:
\(x^2 - 4x + 10 = 0\)
The discriminant (\(b^2 - 4ac\)) is \(16 - 40 = -24\) (not factorable). -
\(x^2 = 2x + 8\)
Rearranging:
\(x^2 - 2x - 8 = 0\)
The discriminant is \(4 + 32 = 36\) (which is a perfect square: \(6^2\)). This can be factored as \((x - 4)(x + 2) = 0\). -
\(-12 = x^2 - x\)
Rearranging:
\(x^2 - x + 12 = 0\)
The discriminant is \((-1)^2 - 4(1)(12) = 1 - 48 = -47\) (not factorable). -
\(x^2 + 9x = 8\)
Rearranging:
\(x^2 + 9x - 8 = 0\)
The discriminant is \(81 + 32 = 113\) (not factorable).
From the analysis, the quadratic equation that can be solved by factoring is:
\(x^2 = 2x + 8\).