Solve left(2x-1right)^2-7(2*-1)+12=0

$${ \left(2x-1 \right) }^{ 2 } -7(2 \times -1)+12=0$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{26}i+1}{2}\approx 0.5-2.549509757i$$

$$x=\frac{1+\sqrt{26}i}{2}\approx 0.5+2.549509757i$$

Steps by Finding Square Root

Subtracting 26 from itself leaves 0.

$$\left(2x-1\right)^{2}=-26$$

Take the square root of both sides of the equation.

$$2x-1=\sqrt{26}i 2x-1=-\sqrt{26}i$$

Add 1 to both sides of the equation.

$$2x-1-\left(-1\right)=\sqrt{26}i-\left(-1\right) 2x-1-\left(-1\right)=-\sqrt{26}i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$2x=\sqrt{26}i-\left(-1\right) 2x=-\sqrt{26}i-\left(-1\right)$$

Subtract -1 from i\sqrt{26}.

$$2x=1+\sqrt{26}i$$

Subtract -1 from -i\sqrt{26}.

$$2x=-\sqrt{26}i+1$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{1+\sqrt{26}i}{2} \frac{2x}{2}=\frac{-\sqrt{26}i+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{1+\sqrt{26}i}{2} x=\frac{-\sqrt{26}i+1}{2}$$