Solve a*4a=4

$$a \cdot 4 a = 4$$

Solve for a

$$a=1$$

$$a=-1$$

Steps by Finding Square Root

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

$$a^{2}\times 4=4$$

Divide both sides by 4.

$$a^{2}=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$a^{2}=1$$

Take the square root of both sides of the equation.

$$a=1 a=-1$$

Steps Using the Quadratic Formula

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

$$a^{2}\times 4=4$$

Subtract 4 from both sides.

$$a^{2}\times 4-4=0$$

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.

$$4a^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$a=\frac{0±\sqrt{-16\left(-4\right)}}{2\times 4}$$

Multiply -16 times -4.

$$a=\frac{0±\sqrt{64}}{2\times 4}$$

Take the square root of 64.

$$a=\frac{0±8}{2\times 4}$$

Multiply 2 times 4.

$$a=\frac{0±8}{8}$$

Now solve the equation a=\frac{0±8}{8} when ± is plus. Divide 8 by 8.

$$a=1$$

Now solve the equation a=\frac{0±8}{8} when ± is minus. Divide -8 by 8.

$$a=-1$$

The equation is now solved.

$$a=1 a=-1$$