Solve x^2=34^2+34^2-(34*34*2*cos(60)

$${ x }^{ 2 } = { 34 }^{ 2 } + { 34 }^{ 2 } -(34 \times 34 \times 2 \times \cos ( 60 )$$

Solve for x (complex solution)

$$x=e^{\pi i}\sqrt{2312-2312\cos(-60)}\approx -67.186150438$$

$$x=e^{\frac{arg(2312-2312\cos(-60))i}{2}}\sqrt{2312-2312\cos(-60)}\approx 67.186150438$$

Steps by Finding Square Root

Calculate 34 to the power of 2 and get 1156.

$$x^{2}=1156+34^{2}-34\times 34\times 2\times \cos(60)$$

Calculate 34 to the power of 2 and get 1156.

$$x^{2}=1156+1156-34\times 34\times 2\times \cos(60)$$

Add 1156 and 1156 to get 2312.

$$x^{2}=2312-34\times 34\times 2\times \cos(60)$$

The equation is now solved.

$$x=34\sqrt{2\left(1-\cos(60)\right)} x=-34\sqrt{2\left(1-\cos(60)\right)}$$

Steps Using the Quadratic Formula

Calculate 34 to the power of 2 and get 1156.

$$x^{2}=1156+34^{2}-34\times 34\times 2\times \cos(60)$$

Calculate 34 to the power of 2 and get 1156.

$$x^{2}=1156+1156-34\times 34\times 2\times \cos(60)$$

Add 1156 and 1156 to get 2312.

$$x^{2}=2312-34\times 34\times 2\times \cos(60)$$

Add 34\times 34\times 2\times \cos(60) to both sides.

$$x^{2}+34\times 34\times 2\times \cos(60)=2312$$

Subtract 2312 from both sides.

$$x^{2}+34\times 34\times 2\times \cos(60)-2312=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+2312\cos(60)-2312=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 2312\left(\cos(60)-1\right) for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2312\left(\cos(60)-1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2312\left(\cos(60)-1\right)}}{2}$$

Multiply -4 times 2312\left(\cos(60)-1\right).

$$x=\frac{0±\sqrt{9248\left(1-\cos(60)\right)}}{2}$$

Take the square root of 9248\left(-\cos(60)+1\right).

$$x=\frac{0±68\sqrt{2\left(1-\cos(60)\right)}}{2}$$

Now solve the equation x=\frac{0±68\sqrt{2\left(1-\cos(60)\right)}}{2} when ± is plus.

$$x=34\sqrt{2\left(1-\cos(60)\right)}$$

Now solve the equation x=\frac{0±68\sqrt{2\left(1-\cos(60)\right)}}{2} when ± is minus.

$$x=-34\sqrt{2\left(1-\cos(60)\right)}$$

The equation is now solved.

$$x=34\sqrt{2\left(1-\cos(60)\right)} x=-34\sqrt{2\left(1-\cos(60)\right)}$$

Solve for x

$$x=34\sqrt{2\left(1-\cos(60)\right)}\approx 67.186150438$$

$$x=-34\sqrt{2\left(1-\cos(60)\right)}\approx -67.186150438$$