Solving a Radical Equation with Absolute Values

Question

Solve the equation
$$\sqrt{16*t^2+48*t+36}-\frac{4*t+6}{\sqrt{t^2+3*t+2.25}}=\frac{t}{2}$$
for $$t.$$
 
Expression | Simplification
---|---
$$\sqrt{16*t^2+48*t+36}$$ | $$|4*t+6|$$
$$\sqrt{t^2+3*t+2.25}$$ | $$|t+1.5|$$
Assuming $$t> -1.5$$, we have: | $$|4*t+6|=4*(t+1.5)$$ and $$|t+1.5|=t+1.5$$
Equation reduction | Leads to: $$4*(t+1.5)-4=\frac{t}{2}$$

Accepted Answer

$$t=-\frac{4}{7}$$

Answer

$$t=\frac{4}{7}$$

Answer

$$t=-\frac{2}{3}$$

Answer

$$t=\frac{2}{3}$$

Expression	Simplification
$$\sqrt{16t^2+48t+36}$$	$$\|4*t+6\|$$
$$\sqrt{t^2+3*t+2.25}$$	$$\|t+1.5\|$$
Assuming $$t> -1.5$$, we have:	$$\|4t+6\|=4(t+1.5)$$ and $$\|t+1.5\|=t+1.5$$
Equation reduction	Leads to: $$4*(t+1.5)-4=\frac{t}{2}$$

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