Solve 5a^2-7=4

$$5 a ^ { 2 } - 7 = 4$$

Solve for a

$$a = \frac{\sqrt{55}}{5} \approx 1.483239697$$

$$a = -\frac{\sqrt{55}}{5} \approx -1.483239697$$

Steps by Finding Square Root

Add 7 to both sides.

$$5a^{2}=4+7$$

Add 4 and 7 to get 11.

$$5a^{2}=11$$

Divide both sides by 5.

$$a^{2}=\frac{11}{5}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{55}}{5} a=-\frac{\sqrt{55}}{5}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$5a^{2}-7-4=0$$

Subtract 4 from -7 to get -11.

$$5a^{2}-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 5\left(-11\right)}}{2\times 5}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 5\left(-11\right)}}{2\times 5}$$

Multiply -4 times 5.

$$a=\frac{0±\sqrt{-20\left(-11\right)}}{2\times 5}$$

Multiply -20 times -11.

$$a=\frac{0±\sqrt{220}}{2\times 5}$$

Take the square root of 220.

$$a=\frac{0±2\sqrt{55}}{2\times 5}$$

Multiply 2 times 5.

$$a=\frac{0±2\sqrt{55}}{10}$$

Now solve the equation a=\frac{0±2\sqrt{55}}{10} when ± is plus.

$$a=\frac{\sqrt{55}}{5}$$

Now solve the equation a=\frac{0±2\sqrt{55}}{10} when ± is minus.

$$a=-\frac{\sqrt{55}}{5}$$

The equation is now solved.

$$a=\frac{\sqrt{55}}{5} a=-\frac{\sqrt{55}}{5}$$