Solve 7x^2*32=4

$$7 x ^ { 2 } \times 32 = 4$$

Solve for x

$$x=\frac{\sqrt{14}}{28}\approx 0.133630621$$

$$x=-\frac{\sqrt{14}}{28}\approx -0.133630621$$

Steps by Finding Square Root

Multiply 7 and 32 to get 224.

$$224x^{2}=4$$

Divide both sides by 224.

$$x^{2}=\frac{4}{224}$$

Reduce the fraction \frac{4}{224} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{1}{56}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{28} x=-\frac{\sqrt{14}}{28}$$

Steps Using the Quadratic Formula

Multiply 7 and 32 to get 224.

$$224x^{2}=4$$

Subtract 4 from both sides.

$$224x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 224 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 224\left(-4\right)}}{2\times 224}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 224\left(-4\right)}}{2\times 224}$$

Multiply -4 times 224.

$$x=\frac{0±\sqrt{-896\left(-4\right)}}{2\times 224}$$

Multiply -896 times -4.

$$x=\frac{0±\sqrt{3584}}{2\times 224}$$

Take the square root of 3584.

$$x=\frac{0±16\sqrt{14}}{2\times 224}$$

Multiply 2 times 224.

$$x=\frac{0±16\sqrt{14}}{448}$$

Now solve the equation x=\frac{0±16\sqrt{14}}{448} when ± is plus.

$$x=\frac{\sqrt{14}}{28}$$

Now solve the equation x=\frac{0±16\sqrt{14}}{448} when ± is minus.

$$x=-\frac{\sqrt{14}}{28}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{28} x=-\frac{\sqrt{14}}{28}$$