Solve x^2+7^2=(2x)^2

$$x ^ { 2 } + 7 ^ { 2 } = ( 2 x ) ^ { 2 }$$

Solve for x

$$x = \frac{7 \sqrt{3}}{3} \approx 4.041451884$$

$$x = -\frac{7 \sqrt{3}}{3} \approx -4.041451884$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=\left(2x\right)^{2}$$

Expand \left(2x\right)^{2}.

$$x^{2}+49=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+49=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+49-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+49=0$$

Subtract 49 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-49$$

Divide both sides by -3.

$$x^{2}=\frac{-49}{-3}$$

Fraction \frac{-49}{-3} can be simplified to \frac{49}{3} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{49}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{3}}{3} x=-\frac{7\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=\left(2x\right)^{2}$$

Expand \left(2x\right)^{2}.

$$x^{2}+49=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+49=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+49-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 49}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 49}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 49}}{2\left(-3\right)}$$

Multiply 12 times 49.

$$x=\frac{0±\sqrt{588}}{2\left(-3\right)}$$

Take the square root of 588.

$$x=\frac{0±14\sqrt{3}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±14\sqrt{3}}{-6}$$

Now solve the equation x=\frac{0±14\sqrt{3}}{-6} when ± is plus.

$$x=-\frac{7\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±14\sqrt{3}}{-6} when ± is minus.

$$x=\frac{7\sqrt{3}}{3}$$

The equation is now solved.

$$x=-\frac{7\sqrt{3}}{3} x=\frac{7\sqrt{3}}{3}$$