What are the approximate solutions of 5x² - 7x = 1, rounded to the nearest hundredth?

Solution:

Given, the equation is 5x² - 7x = 1

The equation can be rewritten as 5x² - 7x - 1 = 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 = 4, b = -7, c = -1

\(x = \frac{-(-7)\pm \sqrt{(-7)^{2}-4(5)(-1)}}{2(5)}\\x=\frac{7\pm \sqrt{49+20}}{10}\\x=\frac{7\pm \sqrt{69}}{10}\)

On solving,

\(x=\frac{7+\sqrt{69}}{10}\)

\(x=\frac{7+8.307}{10}\\x=\frac{15.307}{10}\)

x = 1.5307

Now, \(x=\frac{7-\sqrt{69}}{10}\\x=\frac{7-8.307}{10}\)

x = \(x=\frac{-1.307}{10}\)

x = -0.1307

Therefore, the solutions of 5x² - 7x = 1 are 1.5307 and -0.1307

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What are the approximate solutions of 5x² - 7x = 1, rounded to the nearest hundredth?

Summary:

The approximate solutions of 5x² - 7x = 1, rounded to the nearest hundredth are 1.53 and -0.13