Question

question 7 of 10, step 1 of 1 solve the following quadratic equation by using the quadratic formula. if needed, submit your answer as a fraction reduced to lowest terms or round your answer to two decimal places. 5z² + 10z = 12z - 4 answer z = or

Explanation:

Step1: Rearrange to standard form

$5z^2 + 10z - 12z + 4 = 0$
$5z^2 - 2z + 4 = 0$

Step2: Identify a, b, c

For $az^2+bz+c=0$, $a=5$, $b=-2$, $c=4$

Step3: Apply quadratic formula

Quadratic formula: $z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$z=\frac{-(-2)\pm\sqrt{(-2)^2-4(5)(4)}}{2(5)}$
$z=\frac{2\pm\sqrt{4-80}}{10}$
$z=\frac{2\pm\sqrt{-76}}{10}$
$z=\frac{2\pm2\sqrt{19}i}{10}$
$z=\frac{1\pm\sqrt{19}i}{5}$

Step4: Convert to decimal form

$\sqrt{19}\approx4.3589$, so:
$z=\frac{1+4.3589i}{5}\approx0.20 + 0.87i$
$z=\frac{1-4.3589i}{5}\approx0.20 - 0.87i$

Answer:

$z \approx 0.20 + 0.87i$ or $z \approx 0.20 - 0.87i$
Or as exact fractions: $z=\frac{1+\sqrt{19}i}{5}$ or $z=\frac{1-\sqrt{19}i}{5}$