Solve xsqrt{40}+3cos(4)=70

$$x \sqrt { 40 } + 3 \cos ( 4 ) = 70$$

Solve for x

$$x = \frac{335036539246102637 \sqrt{10}}{100000000000000000} = 10\frac{59478563398076930}{1 \times 10^{17}} \approx 10.594785634$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$x \sqrt{40} + 3 \cdot 0.9975640502598242 = 70$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$x\times 2\sqrt{10}+3\times 0.9975640502598242=70$$

Multiply 3 and 0.9975640502598242 to get 2.9926921507794726.

$$x\times 2\sqrt{10}+2.9926921507794726=70$$

Subtract 2.9926921507794726 from both sides.

$$x\times 2\sqrt{10}=70-2.9926921507794726$$

Subtract 2.9926921507794726 from 70 to get 67.0073078492205274.

$$x\times 2\sqrt{10}=67.0073078492205274$$

The equation is in standard form.

$$2\sqrt{10}x=67.0073078492205274$$

Divide both sides by 2\sqrt{10}.

$$\frac{2\sqrt{10}x}{2\sqrt{10}}=\frac{67.0073078492205274}{2\sqrt{10}}$$

Dividing by 2\sqrt{10} undoes the multiplication by 2\sqrt{10}.

$$x=\frac{67.0073078492205274}{2\sqrt{10}}$$

Divide 67.0073078492205274 by 2\sqrt{10}.

$$x=\frac{335036539246102637\sqrt{10}}{100000000000000000}$$