What are the two solutions of x² - 2x - 4 = -3x + 9?

Solution:

Given, the expression is x² - 2x - 4 = -3x + 9.

We have to find the solutions of the expression.

By grouping,

x² - 2x + 3x  = 9 + 4

x² + x - 13 = 0

Using quadratic  formula,

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

Here, a = 1, b = 1, c = -13

\(x=\frac{-1\pm \sqrt{(1)^{2}-4(1)(-13)}}{2(1)}\\x=\frac{-1\pm \sqrt{1+52}}{2}\\x=\frac{-1\pm \sqrt{53}}{2}\\x=\frac{-1\pm 7.28}{2}\)

So, \(x=\frac{-1+7.28}{2}=\frac{6.28}{2}=3.14\)

\(x=\frac{-1-7.28}{2}=\frac{-8.28}{2}=-4.14\)

Therefore, the solutions are 3.14 and -4.14.

What are the two solutions of x² - 2x - 4 = -3x + 9?

Summary:

The solutions of x² - 2x - 4 = -3x + 9 are 3.14 and -4.14.