Solve x^2-(2k+1)x+7=0

$$x ^ { 2 } - ( 2 k + 1 ) x + 7 = 0$$

Solve for k

$$k=\frac{x}{2}-\frac{1}{2}+\frac{7}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k+1 by x.

$$x^{2}-\left(2kx+x\right)+7=0$$

To find the opposite of 2kx+x, find the opposite of each term.

$$x^{2}-2kx-x+7=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2kx-x+7=-x^{2}$$

Add x to both sides.

$$-2kx+7=-x^{2}+x$$

Subtract 7 from both sides.

$$-2kx=-x^{2}+x-7$$

The equation is in standard form.

$$\left(-2x\right)k=-x^{2}+x-7$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)k}{-2x}=\frac{-x^{2}+x-7}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$k=\frac{-x^{2}+x-7}{-2x}$$

Divide x-x^{2}-7 by -2x.

$$k=\frac{x}{2}-\frac{1}{2}+\frac{7}{2x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4k^{2}+4k-27}}{2}+k+\frac{1}{2}$$

$$x=-\frac{\sqrt{4k^{2}+4k-27}}{2}+k+\frac{1}{2}$$

Solve for x

$$x=\frac{\sqrt{4k^{2}+4k-27}}{2}+k+\frac{1}{2}$$

$$x=-\frac{\sqrt{4k^{2}+4k-27}}{2}+k+\frac{1}{2}\text{, }k\geq \sqrt{7}-\frac{1}{2}\text{ or }k\leq -\sqrt{7}-\frac{1}{2}$$