Solve by the quadratic formula: x2−2x + 5 = 0 (1 point) Responses ±2 ±2 1±2i 1 plus or minus 2 i ±1 plus or minus 1 ±2i
To solve the equation \(x^2 -2x + 5 = 0\) using the quadratic formula, we can identify that \(a = 1\), \(b = -2\), and \(c = 5\).
The quadratic formula states that the solutions to the equation \(ax^2 + bx + c = 0\) are given by:
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
Substituting the values into the formula, we have:
\[x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(5)}}{2(1)}\]
Simplifying,
\[x = \frac{2 \pm \sqrt{4 - 20}}{2}\]
\[x = \frac{2 \pm \sqrt{-16}}{2}\]
\[x = \frac{2 \pm 4i}{2}\]
Reducing,
\[x = 1 \pm 2i\]
Therefore, the solution to the equation \(x^2 -2x + 5 = 0\) is \(1 \pm 2i\).