Solve x56-2x/2=200

$$x \frac { 56 - 2 x } { 2 } = 200$$

Solve for x (complex solution)

$$x=14+2i$$

$$x=14-2i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$x\left(56-2x\right)=400$$

Use the distributive property to multiply x by 56-2x.

$$56x-2x^{2}=400$$

Subtract 400 from both sides.

$$56x-2x^{2}-400=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-2x^{2}+56x-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 56 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-56±\sqrt{56^{2}-4\left(-2\right)\left(-400\right)}}{2\left(-2\right)}$$

Square 56.

$$x=\frac{-56±\sqrt{3136-4\left(-2\right)\left(-400\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-56±\sqrt{3136+8\left(-400\right)}}{2\left(-2\right)}$$

Multiply 8 times -400.

$$x=\frac{-56±\sqrt{3136-3200}}{2\left(-2\right)}$$

Add 3136 to -3200.

$$x=\frac{-56±\sqrt{-64}}{2\left(-2\right)}$$

Take the square root of -64.

$$x=\frac{-56±8i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-56±8i}{-4}$$

Now solve the equation x=\frac{-56±8i}{-4} when ± is plus. Add -56 to 8i.

$$x=\frac{-56+8i}{-4}$$

Divide -56+8i by -4.

$$x=14-2i$$

Now solve the equation x=\frac{-56±8i}{-4} when ± is minus. Subtract 8i from -56.

$$x=\frac{-56-8i}{-4}$$

Divide -56-8i by -4.

$$x=14+2i$$

The equation is now solved.

$$x=14-2i x=14+2i$$

Steps for Completing the Square

Multiply both sides of the equation by 2.

$$x\left(56-2x\right)=400$$

Use the distributive property to multiply x by 56-2x.

$$56x-2x^{2}=400$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-2x^{2}+56x=400$$

Divide both sides by -2.

$$\frac{-2x^{2}+56x}{-2}=\frac{400}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{56}{-2}x=\frac{400}{-2}$$

Divide 56 by -2.

$$x^{2}-28x=\frac{400}{-2}$$

Divide 400 by -2.

$$x^{2}-28x=-200$$

Divide -28, the coefficient of the x term, by 2 to get -14. Then add the square of -14 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-28x+\left(-14\right)^{2}=-200+\left(-14\right)^{2}$$

Square -14.

$$x^{2}-28x+196=-200+196$$

Add -200 to 196.

$$x^{2}-28x+196=-4$$

Factor x^{2}-28x+196. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-14\right)^{2}=-4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{-4}$$

Simplify.

$$x-14=2i x-14=-2i$$

Add 14 to both sides of the equation.

$$x=14+2i x=14-2i$$