Answer
$x=1.52$ and $x=−3.52$
Work Step by Step
Divide both sides by $0.75$: $$x^2+2x=\frac{16}{3}.$$ Add $1$ to both sides to complete the square $$x^2+2x+1=\frac{16}{3}+1.$$ Simplify to $$x^2+2x+1=\frac{19}{3}.$$ Factor the left side to get $$(x+1)^2=\frac{19}{3}.$$
Take the square root and get $$x+1=\pm\sqrt{\frac{19}{3}}.$$ Subtract $1$ from both sides and get $$x = −1\pm \sqrt{\frac{19}{3}}$$ The solutions are $$x_1=-1-\sqrt{\frac{19}{3}}\approx -3.5166$$ $$x_2=-1+\sqrt{\frac{19}{3}}\approx 1.5166.$$ Rounding to the nearest hundredth, we get $x=−3.52$ and $x=1.52$.
