Solve 28*x=2-x^2-20/28=

$$28 \cdot x = \frac { 2 - x ^ { 2 } - 20 } { 28 } =$$

Solve for x (complex solution)

$$x=\sqrt{153646}-392\approx -0.022959856$$

$$x=-\left(\sqrt{153646}+392\right)\approx -783.977040144$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 28.

$$784x=2-x^{2}-20$$

Subtract 20 from 2 to get -18.

$$784x=-18-x^{2}$$

Subtract -18 from both sides.

$$784x-\left(-18\right)=-x^{2}$$

The opposite of -18 is 18.

$$784x+18=-x^{2}$$

Add x^{2} to both sides.

$$784x+18+x^{2}=0$$

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.

$$x^{2}+784x+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 784 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-784±\sqrt{784^{2}-4\times 18}}{2}$$

Square 784.

$$x=\frac{-784±\sqrt{614656-4\times 18}}{2}$$

Multiply -4 times 18.

$$x=\frac{-784±\sqrt{614656-72}}{2}$$

Add 614656 to -72.

$$x=\frac{-784±\sqrt{614584}}{2}$$

Take the square root of 614584.

$$x=\frac{-784±2\sqrt{153646}}{2}$$

Now solve the equation x=\frac{-784±2\sqrt{153646}}{2} when ± is plus. Add -784 to 2\sqrt{153646}.

$$x=\frac{2\sqrt{153646}-784}{2}$$

Divide -784+2\sqrt{153646} by 2.

$$x=\sqrt{153646}-392$$

Now solve the equation x=\frac{-784±2\sqrt{153646}}{2} when ± is minus. Subtract 2\sqrt{153646} from -784.

$$x=\frac{-2\sqrt{153646}-784}{2}$$

Divide -784-2\sqrt{153646} by 2.

$$x=-\sqrt{153646}-392$$

The equation is now solved.

$$x=\sqrt{153646}-392 x=-\sqrt{153646}-392$$

Steps for Completing the Square

Multiply both sides of the equation by 28.

$$784x=2-x^{2}-20$$

Subtract 20 from 2 to get -18.

$$784x=-18-x^{2}$$

Add x^{2} to both sides.

$$784x+x^{2}=-18$$

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.

$$x^{2}+784x=-18$$

Divide 784, the coefficient of the x term, by 2 to get 392. Then add the square of 392 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+784x+392^{2}=-18+392^{2}$$

Square 392.

$$x^{2}+784x+153664=-18+153664$$

Add -18 to 153664.

$$x^{2}+784x+153664=153646$$

Factor x^{2}+784x+153664. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+392\right)^{2}=153646$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+392\right)^{2}}=\sqrt{153646}$$

Simplify.

$$x+392=\sqrt{153646} x+392=-\sqrt{153646}$$

Subtract 392 from both sides of the equation.

$$x=\sqrt{153646}-392 x=-\sqrt{153646}-392$$

Solve for x

$$x=\sqrt{153646}-392\approx -0.022959856$$

$$x=-\sqrt{153646}-392\approx -783.977040144$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 28.

$$784x=2-x^{2}-20$$

Subtract 20 from 2 to get -18.

$$784x=-18-x^{2}$$

Subtract -18 from both sides.

$$784x-\left(-18\right)=-x^{2}$$

The opposite of -18 is 18.

$$784x+18=-x^{2}$$

Add x^{2} to both sides.

$$784x+18+x^{2}=0$$

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.

$$x^{2}+784x+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 784 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-784±\sqrt{784^{2}-4\times 18}}{2}$$

Square 784.

$$x=\frac{-784±\sqrt{614656-4\times 18}}{2}$$

Multiply -4 times 18.

$$x=\frac{-784±\sqrt{614656-72}}{2}$$

Add 614656 to -72.

$$x=\frac{-784±\sqrt{614584}}{2}$$

Take the square root of 614584.

$$x=\frac{-784±2\sqrt{153646}}{2}$$

Now solve the equation x=\frac{-784±2\sqrt{153646}}{2} when ± is plus. Add -784 to 2\sqrt{153646}.

$$x=\frac{2\sqrt{153646}-784}{2}$$

Divide -784+2\sqrt{153646} by 2.

$$x=\sqrt{153646}-392$$

Now solve the equation x=\frac{-784±2\sqrt{153646}}{2} when ± is minus. Subtract 2\sqrt{153646} from -784.

$$x=\frac{-2\sqrt{153646}-784}{2}$$

Divide -784-2\sqrt{153646} by 2.

$$x=-\sqrt{153646}-392$$

The equation is now solved.

$$x=\sqrt{153646}-392 x=-\sqrt{153646}-392$$

Steps for Completing the Square

Multiply both sides of the equation by 28.

$$784x=2-x^{2}-20$$

Subtract 20 from 2 to get -18.

$$784x=-18-x^{2}$$

Add x^{2} to both sides.

$$784x+x^{2}=-18$$

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.

$$x^{2}+784x=-18$$

Divide 784, the coefficient of the x term, by 2 to get 392. Then add the square of 392 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+784x+392^{2}=-18+392^{2}$$

Square 392.

$$x^{2}+784x+153664=-18+153664$$

Add -18 to 153664.

$$x^{2}+784x+153664=153646$$

Factor x^{2}+784x+153664. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+392\right)^{2}=153646$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+392\right)^{2}}=\sqrt{153646}$$

Simplify.

$$x+392=\sqrt{153646} x+392=-\sqrt{153646}$$

Subtract 392 from both sides of the equation.

$$x=\sqrt{153646}-392 x=-\sqrt{153646}-392$$