Solve 4x^2=7^7

$$4 x ^ { 2 } = 7 ^ { 7 }$$

Solve for x

$$x = \frac{343 \sqrt{7}}{2} \approx 453.746349848$$

$$x = -\frac{343 \sqrt{7}}{2} \approx -453.746349848$$

Steps by Finding Square Root

Calculate 7 to the power of 7 and get 823543.

$$4x^{2}=823543$$

Divide both sides by 4.

$$x^{2}=\frac{823543}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{343\sqrt{7}}{2} x=-\frac{343\sqrt{7}}{2}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 7 and get 823543.

$$4x^{2}=823543$$

Subtract 823543 from both sides.

$$4x^{2}-823543=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -823543 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-823543\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-823543\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-823543\right)}}{2\times 4}$$

Multiply -16 times -823543.

$$x=\frac{0±\sqrt{13176688}}{2\times 4}$$

Take the square root of 13176688.

$$x=\frac{0±1372\sqrt{7}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±1372\sqrt{7}}{8}$$

Now solve the equation x=\frac{0±1372\sqrt{7}}{8} when ± is plus.

$$x=\frac{343\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±1372\sqrt{7}}{8} when ± is minus.

$$x=-\frac{343\sqrt{7}}{2}$$

The equation is now solved.

$$x=\frac{343\sqrt{7}}{2} x=-\frac{343\sqrt{7}}{2}$$