Solve -x/8.314=-1176+6.3*10^7(1/450)^2

$$- \frac { x } { 8.314 } = - 1176 + 6.3 \times 10 ^ { 7 } ( \frac { 1 } { 450 } ) ^ { 2 }$$

Solve for x

$$x = \frac{8089522}{1125} = 7190\frac{772}{1125} \approx 7190.686222222$$

Steps for Solving Linear Equation

Calculate 10 to the power of 7 and get 10000000.

$$-\frac{x}{8.314}=-1176+6.3\times 10000000\times \left(\frac{1}{450}\right)^{2}$$

Multiply 6.3 and 10000000 to get 63000000.

$$-\frac{x}{8.314}=-1176+63000000\times \left(\frac{1}{450}\right)^{2}$$

Calculate \frac{1}{450} to the power of 2 and get \frac{1}{202500}.

$$-\frac{x}{8.314}=-1176+63000000\times \frac{1}{202500}$$

Multiply 63000000 and \frac{1}{202500} to get \frac{63000000}{202500}.

$$-\frac{x}{8.314}=-1176+\frac{63000000}{202500}$$

Reduce the fraction \frac{63000000}{202500} to lowest terms by extracting and canceling out 22500.

$$-\frac{x}{8.314}=-1176+\frac{2800}{9}$$

Convert -1176 to fraction -\frac{10584}{9}.

$$-\frac{x}{8.314}=-\frac{10584}{9}+\frac{2800}{9}$$

Since -\frac{10584}{9} and \frac{2800}{9} have the same denominator, add them by adding their numerators.

$$-\frac{x}{8.314}=\frac{-10584+2800}{9}$$

Add -10584 and 2800 to get -7784.

$$-\frac{x}{8.314}=-\frac{7784}{9}$$

Divide both sides by -1.

$$\frac{x}{8.314}=\frac{-\frac{7784}{9}}{-1}$$

Express \frac{-\frac{7784}{9}}{-1} as a single fraction.

$$\frac{x}{8.314}=\frac{-7784}{9\left(-1\right)}$$

Multiply 9 and -1 to get -9.

$$\frac{x}{8.314}=\frac{-7784}{-9}$$

Fraction \frac{-7784}{-9} can be simplified to \frac{7784}{9} by removing the negative sign from both the numerator and the denominator.

$$\frac{x}{8.314}=\frac{7784}{9}$$

Multiply both sides by 8.314.

$$x=\frac{7784}{9}\times 8.314$$

Convert decimal number 8.314 to fraction \frac{8314}{1000}. Reduce the fraction \frac{8314}{1000} to lowest terms by extracting and canceling out 2.

$$x=\frac{7784}{9}\times \frac{4157}{500}$$

Multiply \frac{7784}{9} times \frac{4157}{500} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7784\times 4157}{9\times 500}$$

Do the multiplications in the fraction \frac{7784\times 4157}{9\times 500}.

$$x=\frac{32358088}{4500}$$

Reduce the fraction \frac{32358088}{4500} to lowest terms by extracting and canceling out 4.

$$x=\frac{8089522}{1125}$$