Solve 1/2=sqrt{1--a^2k/a^2}

$$\frac { 1 } { 2 } = \sqrt { 1 - \frac { - a ^ { 2 } k } { a ^ { 2 } } }$$

Solve for k

$$k = -\frac{3}{4} = -0.75$$

$$a\neq 0$$

Steps for Solving Radical Equations

Factor the expressions that are not already factored in \frac{\left(-a^{2}\right)k}{a^{2}}.

$$\frac{1}{2}=\sqrt{1-\frac{-ka^{2}}{a^{2}}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{1}{2}=\sqrt{1-\left(-k\right)}$$

The opposite of -k is k.

$$\frac{1}{2}=\sqrt{1+k}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{1+k}=\frac{1}{2}$$

Square both sides of the equation.

$$k+1=\frac{1}{4}$$

Subtract 1 from both sides of the equation.

$$k+1-1=\frac{1}{4}-1$$

Subtracting 1 from itself leaves 0.

$$k=\frac{1}{4}-1$$

Subtract 1 from \frac{1}{4}.

$$k=-\frac{3}{4}$$

Solve for a

$$a\neq 0$$

$$k=-\frac{3}{4}\text{ and }a\neq 0$$