Solve ksqrt{28}-sqrt{63}+sqrt{7}=0

$$k \sqrt { 28 } - \sqrt { 63 } + \sqrt { 7 } = 0$$

Solve for k

$$k=1$$

Steps for Solving Linear Equation

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$k\times 2\sqrt{7}-\sqrt{63}+\sqrt{7}=0$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$k\times 2\sqrt{7}-3\sqrt{7}+\sqrt{7}=0$$

Combine -3\sqrt{7} and \sqrt{7} to get -2\sqrt{7}.

$$k\times 2\sqrt{7}-2\sqrt{7}=0$$

Add 2\sqrt{7} to both sides. Anything plus zero gives itself.

$$k\times 2\sqrt{7}=2\sqrt{7}$$

Cancel out 2 on both sides.

$$k\sqrt{7}=\sqrt{7}$$

The equation is in standard form.

$$\sqrt{7}k=\sqrt{7}$$

Divide both sides by \sqrt{7}.

$$\frac{\sqrt{7}k}{\sqrt{7}}=\frac{\sqrt{7}}{\sqrt{7}}$$

Dividing by \sqrt{7} undoes the multiplication by \sqrt{7}.

$$k=\frac{\sqrt{7}}{\sqrt{7}}$$

Divide \sqrt{7} by \sqrt{7}.

$$k=1$$