Question

solve the equation ( x^2 - 3x - 22 = 0 ) to the nearest tenth.

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=-3$, $c=-22$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-22)}}{2(1)}$$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{9 + 88}=\sqrt{97}\approx9.849$

Step4: Compute two solutions

First solution (plus):
$x=\frac{3 + 9.849}{2}=\frac{12.849}{2}\approx6.4$
Second solution (minus):
$x=\frac{3 - 9.849}{2}=\frac{-6.849}{2}\approx-3.4$

Answer:

$x\approx6.4$ and $x\approx-3.4$