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Chapter 11: Problem 5

Solve the quadratic equation \(5 x^{2}-11 x+13=0\)

Short Answer

Expert verified
Answer: The solutions to the quadratic equation are: \(x_1 = \frac{11 + \sqrt{-139}}{10}\) and \(x_2 = \frac{11 - \sqrt{-139}}{10}\).

Step by step solution

01

Identify coefficients a, b, and c

In the given quadratic equation \(5x^{2} - 11x + 13 = 0\), the coefficients are: a = 5 b = -11 c = 13
02

Substitute the coefficients into the quadratic formula

Now, we can substitute the values of a, b, and c into the quadratic formula: x = \(\frac{-(-11) \pm \sqrt{(-11)^2 - 4(5)(13)}}{2(5)}\)
03

Simplify the expression

Let's simplify the expression: x = \(\frac{11 \pm \sqrt{121 - 260}}{10}\) x = \(\frac{11 \pm \sqrt{-139}}{10}\)
04

Write the final solution

Since there are no real solutions due to having the negative number inside the square root, the final solution remains in a complex form: x = \(\frac{11 \pm \sqrt{-139}}{10}\) The solutions to the quadratic equation \(5x^{2} - 11x + 13 = 0\) are: \(x_1 = \frac{11 + \sqrt{-139}}{10}\) and \(x_2 = \frac{11 - \sqrt{-139}}{10}\).

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