How do you solve 4(x-4)^(3/2)=-6?

May 7, 2018

Answer:

color(purple)(x = 4 + root3 (9/4)

Explanation:

$4 {\left(x - 4\right)}^{\frac{3}{2}} = - 6$

color(blue)("Squaring both sides",

${\left(4 {\left(x - 4\right)}^{\frac{3}{2}}\right)}^{2} = {\left(- 6\right)}^{2}$

${4}^{2} \cdot {\left(x - 4\right)}^{\frac{3 \cdot 2}{2}} = 36$

${4}^{2} \cdot {\left(x - 4\right)}^{3} = 36$

${\left(x - 4\right)}^{3} = \frac{36}{16} = \frac{9}{4}$

$x - 4 = {\left(\frac{9}{4}\right)}^{\frac{1}{3}} , \text{ taking cube root on both sides}$

color(purple)(x = 4 + root3 (9/4)