Solve 4^3*7x^2/2=21

$$\frac { 4 ^ { 3 } \cdot 7 x ^ { 2 } } { 2 } = 21$$

Solve for x

$$x=\frac{\sqrt{6}}{8}\approx 0.306186218$$

$$x=-\frac{\sqrt{6}}{8}\approx -0.306186218$$

Steps by Finding Square Root

Multiply both sides by 2.

$$4^{3}\times 7x^{2}=21\times 2$$

Calculate 4 to the power of 3 and get 64.

$$64\times 7x^{2}=21\times 2$$

Multiply 64 and 7 to get 448.

$$448x^{2}=21\times 2$$

Multiply 21 and 2 to get 42.

$$448x^{2}=42$$

Divide both sides by 448.

$$x^{2}=\frac{42}{448}$$

Reduce the fraction \frac{42}{448} to lowest terms by extracting and canceling out 14.

$$x^{2}=\frac{3}{32}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{8} x=-\frac{\sqrt{6}}{8}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$4^{3}\times 7x^{2}=21\times 2$$

Calculate 4 to the power of 3 and get 64.

$$64\times 7x^{2}=21\times 2$$

Multiply 64 and 7 to get 448.

$$448x^{2}=21\times 2$$

Multiply 21 and 2 to get 42.

$$448x^{2}=42$$

Subtract 42 from both sides.

$$448x^{2}-42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 448 for a, 0 for b, and -42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 448\left(-42\right)}}{2\times 448}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 448\left(-42\right)}}{2\times 448}$$

Multiply -4 times 448.

$$x=\frac{0±\sqrt{-1792\left(-42\right)}}{2\times 448}$$

Multiply -1792 times -42.

$$x=\frac{0±\sqrt{75264}}{2\times 448}$$

Take the square root of 75264.

$$x=\frac{0±112\sqrt{6}}{2\times 448}$$

Multiply 2 times 448.

$$x=\frac{0±112\sqrt{6}}{896}$$

Now solve the equation x=\frac{0±112\sqrt{6}}{896} when ± is plus.

$$x=\frac{\sqrt{6}}{8}$$

Now solve the equation x=\frac{0±112\sqrt{6}}{896} when ± is minus.

$$x=-\frac{\sqrt{6}}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{8} x=-\frac{\sqrt{6}}{8}$$