Solve 4x^2-4=41/14

$$4 x ^ { 2 } - 4 = 4 \frac { 1 } { 1 } 4$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Multiply 4 and 1 to get 4.

$$4x^{2}-4=\frac{4+1}{1}\times 4$$

Add 4 and 1 to get 5.

$$4x^{2}-4=\frac{5}{1}\times 4$$

Anything divided by one gives itself.

$$4x^{2}-4=5\times 4$$

Multiply 5 and 4 to get 20.

$$4x^{2}-4=20$$

Add 4 to both sides.

$$4x^{2}=20+4$$

Add 20 and 4 to get 24.

$$4x^{2}=24$$

Divide both sides by 4.

$$x^{2}=\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Multiply 4 and 1 to get 4.

$$4x^{2}-4=\frac{4+1}{1}\times 4$$

Add 4 and 1 to get 5.

$$4x^{2}-4=\frac{5}{1}\times 4$$

Anything divided by one gives itself.

$$4x^{2}-4=5\times 4$$

Multiply 5 and 4 to get 20.

$$4x^{2}-4=20$$

Subtract 20 from both sides.

$$4x^{2}-4-20=0$$

Subtract 20 from -4 to get -24.

$$4x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-24\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-24\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-24\right)}}{2\times 4}$$

Multiply -16 times -24.

$$x=\frac{0±\sqrt{384}}{2\times 4}$$

Take the square root of 384.

$$x=\frac{0±8\sqrt{6}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{6}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$