通过配方法解方程 $x^2 + 5x - 16 = 0$。 给出精确到两位小数的解。

1. Move the constant term to the other side.

$x^2+5x-16=0$

$x^2+5x=16$

2. Complete the square on the left-hand side.

Half of $5$ is $\dfrac{5}{2}$.

$x^2+5x=\left(x+\dfrac{5}{2}\right)^2-\left(\dfrac{5}{2}\right)^2$

So
$\left(x+\dfrac{5}{2}\right)^2-\dfrac{25}{4}=16$

3. Isolate the squared expression and take square roots.

$\left(x+\dfrac{5}{2}\right)^2=16+\dfrac{25}{4}$

$\left(x+\dfrac{5}{2}\right)^2=\dfrac{89}{4}$

$x+\dfrac{5}{2}=\pm \sqrt{\dfrac{89}{4}}=\pm \dfrac{\sqrt{89}}{2}$

4. Find both solutions and round to two decimal places.

$x=-\dfrac{5}{2}\pm\dfrac{\sqrt{89}}{2}$

$x=\dfrac{-5+\sqrt{89}}{2}\quad \text{or}\quad x=\dfrac{-5-\sqrt{89}}{2}$

Using a calculator,
$x=2.216\ldots \quad \text{or}\quad x=-7.216\ldots$

Correct to two decimal places,
$x=2.22\quad \text{or}\quad x=-7.22$