Solve (30+A)*A=304

$$( 30 + A ) \times A = 304$$

Solve for A

$$A=-38$$

$$A=8$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 30+A by A.

$$30A+A^{2}=304$$

Subtract 304 from both sides.

$$30A+A^{2}-304=0$$

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.

$$A^{2}+30A-304=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 30 for b, and -304 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{-30±\sqrt{30^{2}-4\left(-304\right)}}{2}$$

Square 30.

$$A=\frac{-30±\sqrt{900-4\left(-304\right)}}{2}$$

Multiply -4 times -304.

$$A=\frac{-30±\sqrt{900+1216}}{2}$$

Add 900 to 1216.

$$A=\frac{-30±\sqrt{2116}}{2}$$

Take the square root of 2116.

$$A=\frac{-30±46}{2}$$

Now solve the equation A=\frac{-30±46}{2} when ± is plus. Add -30 to 46.

$$A=\frac{16}{2}$$

Divide 16 by 2.

$$A=8$$

Now solve the equation A=\frac{-30±46}{2} when ± is minus. Subtract 46 from -30.

$$A=-\frac{76}{2}$$

Divide -76 by 2.

$$A=-38$$

The equation is now solved.

$$A=8 A=-38$$

Steps for Completing the Square

Use the distributive property to multiply 30+A by A.

$$30A+A^{2}=304$$

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.

$$A^{2}+30A=304$$

Divide 30, the coefficient of the x term, by 2 to get 15. Then add the square of 15 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$A^{2}+30A+15^{2}=304+15^{2}$$

Square 15.

$$A^{2}+30A+225=304+225$$

Add 304 to 225.

$$A^{2}+30A+225=529$$

Factor A^{2}+30A+225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(A+15\right)^{2}=529$$

Take the square root of both sides of the equation.

$$\sqrt{\left(A+15\right)^{2}}=\sqrt{529}$$

Simplify.

$$A+15=23 A+15=-23$$

Subtract 15 from both sides of the equation.

$$A=8 A=-38$$