Solve 4left(x-1right)-xleft(x+4right)=-2

$$4 \left( x-1 \right) -x \left( x+4 \right) =-2$$

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Use the distributive property to multiply 4 by x-1.

$$4x-4-x\left(x+4\right)=-2$$

Use the distributive property to multiply x by x+4.

$$4x-4-\left(x^{2}+4x\right)=-2$$

To find the opposite of x^{2}+4x, find the opposite of each term.

$$4x-4-x^{2}-4x=-2$$

Combine 4x and -4x to get 0.

$$-4-x^{2}=-2$$

Add 4 to both sides.

$$-x^{2}=-2+4$$

Add -2 and 4 to get 2.

$$-x^{2}=2$$

Divide both sides by -1.

$$x^{2}=-2$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Use the distributive property to multiply 4 by x-1.

$$4x-4-x\left(x+4\right)=-2$$

Use the distributive property to multiply x by x+4.

$$4x-4-\left(x^{2}+4x\right)=-2$$

To find the opposite of x^{2}+4x, find the opposite of each term.

$$4x-4-x^{2}-4x=-2$$

Combine 4x and -4x to get 0.

$$-4-x^{2}=-2$$

Add 2 to both sides.

$$-4-x^{2}+2=0$$

Add -4 and 2 to get -2.

$$-2-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-2\right)}}{2\left(-1\right)}$$

Multiply 4 times -2.

$$x=\frac{0±\sqrt{-8}}{2\left(-1\right)}$$

Take the square root of -8.

$$x=\frac{0±2\sqrt{2}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{2}i}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{-2} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{2}i}{-2} when ± is minus.

$$x=\sqrt{2}i$$

The equation is now solved.

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