Solve x^2=3^2+4^2-2*3*4cos39^circ

$$x ^ { 2 } = 3 ^ { 2 } + 4 ^ { 2 } - 2 \times 3 \times 4 \cos 39 ^ { \circ }$$

Solve for x

$$x = \frac{\sqrt{15871242312581746}}{50000000} \approx 2.519622377$$

$$x = -\frac{\sqrt{15871242312581746}}{50000000} \approx -2.519622377$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$x ^ {2} = 3 ^ {2} + 4 ^ {2} - 2 \cdot 3 \cdot 4 \cdot 0.7771459614569709$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=9+4^{2}-2\times 3\times 4\times 0.7771459614569709$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=9+16-2\times 3\times 4\times 0.7771459614569709$$

Add 9 and 16 to get 25.

$$x^{2}=25-2\times 3\times 4\times 0.7771459614569709$$

Multiply 2 and 3 to get 6.

$$x^{2}=25-6\times 4\times 0.7771459614569709$$

Multiply 6 and 4 to get 24.

$$x^{2}=25-24\times 0.7771459614569709$$

Multiply 24 and 0.7771459614569709 to get 18.6515030749673016.

$$x^{2}=25-18.6515030749673016$$

Subtract 18.6515030749673016 from 25 to get 6.3484969250326984.

$$x^{2}=6.3484969250326984$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15871242312581746}}{50000000} x=-\frac{\sqrt{15871242312581746}}{50000000}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$x ^ {2} = 3 ^ {2} + 4 ^ {2} - 2 \cdot 3 \cdot 4 \cdot 0.7771459614569709$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=9+4^{2}-2\times 3\times 4\times 0.7771459614569709$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=9+16-2\times 3\times 4\times 0.7771459614569709$$

Add 9 and 16 to get 25.

$$x^{2}=25-2\times 3\times 4\times 0.7771459614569709$$

Multiply 2 and 3 to get 6.

$$x^{2}=25-6\times 4\times 0.7771459614569709$$

Multiply 6 and 4 to get 24.

$$x^{2}=25-24\times 0.7771459614569709$$

Multiply 24 and 0.7771459614569709 to get 18.6515030749673016.

$$x^{2}=25-18.6515030749673016$$

Subtract 18.6515030749673016 from 25 to get 6.3484969250326984.

$$x^{2}=6.3484969250326984$$

Subtract 6.3484969250326984 from both sides.

$$x^{2}-6.3484969250326984=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6.3484969250326984 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6.3484969250326984\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6.3484969250326984\right)}}{2}$$

Multiply -4 times -6.3484969250326984.

$$x=\frac{0±\sqrt{25.3939877001307936}}{2}$$

Take the square root of 25.3939877001307936.

$$x=\frac{0±\frac{\sqrt{15871242312581746}}{25000000}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{15871242312581746}}{25000000}}{2} when ± is plus.

$$x=\frac{\sqrt{15871242312581746}}{50000000}$$

Now solve the equation x=\frac{0±\frac{\sqrt{15871242312581746}}{25000000}}{2} when ± is minus.

$$x=-\frac{\sqrt{15871242312581746}}{50000000}$$

The equation is now solved.

$$x=\frac{\sqrt{15871242312581746}}{50000000} x=-\frac{\sqrt{15871242312581746}}{50000000}$$