Solve -7ax^2-8ax+100a+1/25x=1/25

$$-7a { x }^{ 2 } -8ax+100a+ \frac{ 1 }{ 25x } = \frac{ 1 }{ 25 }$$

Solve for a

$$a=-\frac{1-x}{25x\left(100-8x-7x^{2}\right)}$$

$$x\neq \frac{2\sqrt{179}-4}{7}\text{ and }x\neq \frac{-2\sqrt{179}-4}{7}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 25x, the least common multiple of 25x,25.

$$-7ax^{2}\times 25x-8ax\times 25x+100a\times 25x+1=x$$

Multiply -7 and 25 to get -175.

$$-175ax^{2}x-8ax\times 25x+100a\times 25x+1=x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-175ax^{3}-8ax\times 25x+100a\times 25x+1=x$$

Multiply x and x to get x^{2}.

$$-175ax^{3}-8ax^{2}\times 25+100a\times 25x+1=x$$

Multiply -8 and 25 to get -200.

$$-175ax^{3}-200ax^{2}+100a\times 25x+1=x$$

Multiply 100 and 25 to get 2500.

$$-175ax^{3}-200ax^{2}+2500ax+1=x$$

Subtract 1 from both sides.

$$-175ax^{3}-200ax^{2}+2500ax=x-1$$

Combine all terms containing a.

$$\left(-175x^{3}-200x^{2}+2500x\right)a=x-1$$

The equation is in standard form.

$$\left(2500x-200x^{2}-175x^{3}\right)a=x-1$$

Divide both sides by 2500x-175x^{3}-200x^{2}.

$$\frac{\left(2500x-200x^{2}-175x^{3}\right)a}{2500x-200x^{2}-175x^{3}}=\frac{x-1}{2500x-200x^{2}-175x^{3}}$$

Dividing by 2500x-175x^{3}-200x^{2} undoes the multiplication by 2500x-175x^{3}-200x^{2}.

$$a=\frac{x-1}{2500x-200x^{2}-175x^{3}}$$

Divide x-1 by 2500x-175x^{3}-200x^{2}.

$$a=\frac{x-1}{25x\left(100-8x-7x^{2}\right)}$$