Question

solve the quadratic equation. (enter your answers as a comma-separated list.)
2x² - 4x + 37 = 0
x =
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Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 2\), \(b = -4\), \(c = 37\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Calculate discriminant \(\Delta = b^2 - 4ac = (-4)^2 - 4\times2\times37 = 16 - 296 = -280\).
Since \(\Delta<0\), roots are complex: \(x=\frac{4\pm\sqrt{-280}}{4}=\frac{4\pm2i\sqrt{70}}{4}=1\pm\frac{i\sqrt{70}}{2}\).

Answer:

\(1 - \frac{i\sqrt{70}}{2}, 1 + \frac{i\sqrt{70}}{2}\)