Solve 4^2(x-5)=25(x-a)

$$4 ^ { 2 } ( x - 5 ) = 25 ( x - a )$$

Solve for a

$$a=\frac{9x}{25}+\frac{16}{5}$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16\left(x-5\right)=25\left(x-a\right)$$

Use the distributive property to multiply 16 by x-5.

$$16x-80=25\left(x-a\right)$$

Use the distributive property to multiply 25 by x-a.

$$16x-80=25x-25a$$

Swap sides so that all variable terms are on the left hand side.

$$25x-25a=16x-80$$

Subtract 25x from both sides.

$$-25a=16x-80-25x$$

Combine 16x and -25x to get -9x.

$$-25a=-9x-80$$

Divide both sides by -25.

$$\frac{-25a}{-25}=\frac{-9x-80}{-25}$$

Dividing by -25 undoes the multiplication by -25.

$$a=\frac{-9x-80}{-25}$$

Divide -9x-80 by -25.

$$a=\frac{9x}{25}+\frac{16}{5}$$

Solve for x

$$x=\frac{25a-80}{9}$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16\left(x-5\right)=25\left(x-a\right)$$

Use the distributive property to multiply 16 by x-5.

$$16x-80=25\left(x-a\right)$$

Use the distributive property to multiply 25 by x-a.

$$16x-80=25x-25a$$

Subtract 25x from both sides.

$$16x-80-25x=-25a$$

Combine 16x and -25x to get -9x.

$$-9x-80=-25a$$

Add 80 to both sides.

$$-9x=-25a+80$$

The equation is in standard form.

$$-9x=80-25a$$

Divide both sides by -9.

$$\frac{-9x}{-9}=\frac{80-25a}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$x=\frac{80-25a}{-9}$$

Divide -25a+80 by -9.

$$x=\frac{25a-80}{9}$$