What are the approximate solutions of 4x² + 2x = 17, rounded to the nearest hundredth.

Solution:

Given, the quadratic equation is 4x² + 2x = 17.

We have to find the approximate solutions of the given equation.

Using quadratic formula to find the roots,

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

The equation can be rewritten as 4x² + 2x - 17 = 0

Here a = 4, b = 2, c = -17

So, \(x=\frac{-2\pm \sqrt{(2)^{2}-4(4)(-17)}}{2(4)}\\x=\frac{-2\pm \sqrt{4+16(17)}}{8}\\x=\frac{-2\pm \sqrt{4+272}}{8}\\x=\frac{-2\pm \sqrt{276}}{8}\)

\(x=\frac{-2\pm 16.61}{8}\)

\(x=\frac{-2+16.61}{8}\\x=\frac{14.61}{8}\\x=1.83\)

\(x=\frac{-2-16.61}{8}\\x=\frac{-18.61}{8}\\x=-2.33\)

Therefore, the solutions are 1.83 and -2.33

What are the approximate solutions of 4x² + 2x = 17, rounded to the nearest hundredth.

Summary:

The approximate solutions of 4x² + 2x = 17, rounded to the nearest hundredth are -2.33 and 1.83