Question

solve the quadratic equation.
( x^2 - 10x - 4 = 0 )
write one exact, simplified solution in each box. you can add or remove boxes. if a solution is
not a real number, write it in the form ( a + bi ) or ( a - bi ), where ( a ) and ( b ) are real numbers.

Explanation:

Step1: Identify coefficients for quadratic formula

For the quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = -10\), \(c = -4\).

Step2: Apply quadratic formula \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

First, calculate the discriminant \(\Delta=b^2 - 4ac=(-10)^2-4\times1\times(-4)=100 + 16 = 116\).
Then, \(x=\frac{-(-10)\pm\sqrt{116}}{2\times1}=\frac{10\pm2\sqrt{29}}{2}=5\pm\sqrt{29}\).

Answer:

\(5 + \sqrt{29}\), \(5 - \sqrt{29}\)