Question

solve using the quadratic formula.
$4g^2 - 4g - 4 = 0$
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
$g = \square$ or $g = \square$

Explanation:

Step1: Identify a,b,c from equation

For $4g^2 -4g -4=0$, $a=4$, $b=-4$, $c=-4$

Step2: Recall quadratic formula

$$g=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Compute discriminant

$$b^2-4ac=(-4)^2-4(4)(-4)=16+64=80$$

Step4: Simplify square root

$\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}$

Step5: Substitute into formula

$$g=\frac{4\pm4\sqrt{5}}{8}=\frac{1\pm\sqrt{5}}{2}$$

Step6: Calculate decimal values

$\frac{1+\sqrt{5}}{2}\approx\frac{1+2.24}{2}=1.62$, $\frac{1-\sqrt{5}}{2}\approx\frac{1-2.24}{2}=-0.62$

Answer:

$g = \frac{1+\sqrt{5}}{2}$ or $g = \frac{1-\sqrt{5}}{2}$
(or as decimals: $g=1.62$ or $g=-0.62$)