Solve {left(sqrt{1.69}-0.6frac{sqrt{19.6}}{2}xright)}^2

$${ \left( \sqrt{ 1.69 } -0.6 \frac{ \sqrt{ 19.6 } }{ 2 } x \right) }^{ 2 }$$

Evaluate

$$\frac{\left(-21\sqrt{10}x+65\right)^{2}}{2500}$$

Solution Steps

Calculate the square root of 1.69 and get 1.3.

$$\left(1.3-0.6\times \frac{\sqrt{19.6}}{2}x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1.3-0.6\times \frac{\sqrt{19.6}}{2}x\right)^{2}.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \left(\frac{\sqrt{19.6}}{2}\right)^{2}x^{2}$$

To raise \frac{\sqrt{19.6}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{\left(\sqrt{19.6}\right)^{2}}{2^{2}}x^{2}$$

The square of \sqrt{19.6} is 19.6.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{19.6}{2^{2}}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{19.6}{4}x^{2}$$

Expand \frac{19.6}{4} by multiplying both numerator and the denominator by 10.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{196}{40}x^{2}$$

Reduce the fraction \frac{196}{40} to lowest terms by extracting and canceling out 4.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{49}{10}x^{2}$$

Multiply 0.36 and \frac{49}{10} to get \frac{441}{250}.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+\frac{441}{250}x^{2}$$

Expand

$$\frac{441x^{2}}{250}-\frac{273\sqrt{10}x}{250}+1.69$$

Solution Steps

Calculate the square root of 1.69 and get 1.3.

$$\left(1.3-0.6\times \frac{\sqrt{19.6}}{2}x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1.3-0.6\times \frac{\sqrt{19.6}}{2}x\right)^{2}.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \left(\frac{\sqrt{19.6}}{2}\right)^{2}x^{2}$$

To raise \frac{\sqrt{19.6}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{\left(\sqrt{19.6}\right)^{2}}{2^{2}}x^{2}$$

The square of \sqrt{19.6} is 19.6.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{19.6}{2^{2}}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{19.6}{4}x^{2}$$

Expand \frac{19.6}{4} by multiplying both numerator and the denominator by 10.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{196}{40}x^{2}$$

Reduce the fraction \frac{196}{40} to lowest terms by extracting and canceling out 4.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+0.36\times \frac{49}{10}x^{2}$$

Multiply 0.36 and \frac{49}{10} to get \frac{441}{250}.

$$1.69-1.56\times \frac{\sqrt{19.6}}{2}x+\frac{441}{250}x^{2}$$