Solve AdivA=7A

$$A \div A = 7 A$$

Solve for A

$$A=\frac{1}{7}\approx 0.142857143$$

Steps Using Factoring

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A.

$$A=7AA$$

Multiply A and A to get A^{2}.

$$A=7A^{2}$$

Subtract 7A^{2} from both sides.

$$A-7A^{2}=0$$

Factor out A.

$$A\left(1-7A\right)=0$$

To find equation solutions, solve A=0 and 1-7A=0.

$$A=0 A=\frac{1}{7}$$

Variable A cannot be equal to 0.

$$A=\frac{1}{7}$$

Steps Using the Quadratic Formula

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A.

$$A=7AA$$

Multiply A and A to get A^{2}.

$$A=7A^{2}$$

Subtract 7A^{2} from both sides.

$$A-7A^{2}=0$$

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.

$$-7A^{2}+A=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{-1±\sqrt{1^{2}}}{2\left(-7\right)}$$

Take the square root of 1^{2}.

$$A=\frac{-1±1}{2\left(-7\right)}$$

Multiply 2 times -7.

$$A=\frac{-1±1}{-14}$$

Now solve the equation A=\frac{-1±1}{-14} when ± is plus. Add -1 to 1.

$$A=\frac{0}{-14}$$

Divide 0 by -14.

$$A=0$$

Now solve the equation A=\frac{-1±1}{-14} when ± is minus. Subtract 1 from -1.

$$A=-\frac{2}{-14}$$

Reduce the fraction \frac{-2}{-14} to lowest terms by extracting and canceling out 2.

$$A=\frac{1}{7}$$

The equation is now solved.

$$A=0 A=\frac{1}{7}$$

Variable A cannot be equal to 0.

$$A=\frac{1}{7}$$

Steps for Completing the Square

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A.

$$A=7AA$$

Multiply A and A to get A^{2}.

$$A=7A^{2}$$

Subtract 7A^{2} from both sides.

$$A-7A^{2}=0$$

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.

$$-7A^{2}+A=0$$

Divide both sides by -7.

$$\frac{-7A^{2}+A}{-7}=\frac{0}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$A^{2}+\frac{1}{-7}A=\frac{0}{-7}$$

Divide 1 by -7.

$$A^{2}-\frac{1}{7}A=\frac{0}{-7}$$

Divide 0 by -7.

$$A^{2}-\frac{1}{7}A=0$$

Divide -\frac{1}{7}, the coefficient of the x term, by 2 to get -\frac{1}{14}. Then add the square of -\frac{1}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$A^{2}-\frac{1}{7}A+\left(-\frac{1}{14}\right)^{2}=\left(-\frac{1}{14}\right)^{2}$$

Square -\frac{1}{14} by squaring both the numerator and the denominator of the fraction.

$$A^{2}-\frac{1}{7}A+\frac{1}{196}=\frac{1}{196}$$

Factor A^{2}-\frac{1}{7}A+\frac{1}{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}.

$$\left(A-\frac{1}{14}\right)^{2}=\frac{1}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(A-\frac{1}{14}\right)^{2}}=\sqrt{\frac{1}{196}}$$

Simplify.

$$A-\frac{1}{14}=\frac{1}{14} A-\frac{1}{14}=-\frac{1}{14}$$

Add \frac{1}{14} to both sides of the equation.

$$A=\frac{1}{7} A=0$$

Variable A cannot be equal to 0.

$$A=\frac{1}{7}$$