What are the approximate solutions of 2x² - 7x = 3, rounded to the nearest hundredth?

Solution:

Given, the equation is 2x² -7x = 3

The equation can be rewritten as 2x² - 7x - 3 = 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 = -7, c = -3

\(x = \frac{-(-7)\pm \sqrt{(-7)^{2}-4(2)(-3)}}{2(2)}\)

\(x = \frac{7\pm \sqrt{49+24}}{4}\)

\(x = \frac{7\pm \sqrt{73}}{4}\)

\(x = \frac{7\pm 8.544}{4}\)

When \(x = \frac{7+8.544}{4}\\x=\frac{15.544}{4}\\x=3.89\)

When \(x = \frac{7-8.544}{4}\\x=\frac{-1.544}{4}\\x=-0.39\)

Therefore, the approximate solutions rounded to the nearest hundredth are x = 3.89 and x = -0.39.

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What are the approximate solutions of 2x² - 7x = 3, rounded to the nearest hundredth?

Summary:

The approximate solutions of 2x² - 7x = 3, rounded to the nearest hundredth are x = 3.89 and x = -0.39.