What are the approximate solutions of 2x² + x = 14, rounded to the nearest hundredth?

Solution:

Given, the equation is 2x² + x = 14

The equation can be rewritten as 2x² + x - 14 = 0

We have to find the solution of the equation.

By using the formula,

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

Here, a = 2, b = 1, c = -14

\(x = \frac{-1\pm \sqrt{(1)^{2}-4(2)(-14)}}{2(2)}\)

\(x = \frac{-1\pm \sqrt{(1)^{2}+112}}{4}\)

\(x = \frac{-1\pm \sqrt{113}}{4}\)

\(x = \frac{-1\pm 10.63}{4}\)

When \(x = \frac{-1+10.63}{4}\\x=\frac{9.63}{4}\\x=2.4075\)

When \(x = \frac{-1-10.63}{4}\\x=\frac{-11.63}{4}\\x=-2.907\)

Therefore, the approximate solutions rounded to the nearest hundredth are x = 2.41 and x = -2.91.

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What are the approximate solutions of 2x² + x = 14, rounded to the nearest hundredth?

Summary:

The approximate solutions of 2x² + x = 14, rounded to the nearest hundredth are x = 2.41 and x = -2.91.