What are the approximate solutions of 2x² + 9x = 8 to the nearest hundredth?

Solution:

Given, the equation is 2x² + 9x = 8.

We have to find the approximate solution to the equation.

The equation can be written as 2x² + 9x - 8 = 0.

Using the quadratic formula,

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

Here, a = 2, b = 9 and c = -8.

\(x=\frac{-9\pm \sqrt{(9)^{2}-4(2)(-8)}}{2(2)}\)

\(x=\frac{-9\pm \sqrt{81+64}}{4}\)

\(x=\frac{-9\pm \sqrt{145}}{4}\)

\(x=\frac{-9\pm 12.04}{4}\)

Now, \(x=\frac{-9+12.04}{4}\\x=\frac{3.04}{4}\\x=0.76\)

\(x=\frac{-9-12.04}{4}\\x=\frac{-21.04}{4}\\x=-5.26\)

Therefore, the approximate solutions to the equation are 0.76 and -5.26

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What are the approximate solutions of 2x² + 9x = 8 to the nearest hundredth?

Summary:

The approximate solutions of 2x² + 9x = 8 to the nearest hundredth are 0.76 and -5.26