+0

# algebra question

0
1
40
1

Find all values of  x such that x/(x + 4) = -8/(x + 7). If you find more than one value, then list your solutions in increasing order, separated by commas.

Dec 30, 2020

#1
+10805
+1

Find all values of x such that x/(x + 4) = -8/(x + 7). If you find more than one value, then list your solutions in increasing order, separated by commas.

Hello Guest!

$$\color{BrickRed}\frac{x}{x+4}=\frac{-8}{x+7}\\ x^2+7x=-8x-32\\ x^2+15x+32=0$$

p          q

$$x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=-7.5\pm\sqrt{7.5^2-32}\\ x=-7.5\pm \sqrt{\frac{97}{4}}\\ x=-7.5\pm 0.5\sqrt{97}\\ x=-7,5\pm 4.9244$$

$$x\in\{-12.42443,-2.57557\}$$

!

Dec 30, 2020
edited by asinus  Dec 30, 2020