5×2⋅5-4x=3125

Use the power rule aman=am+n to combine exponents.

5×2-4x=3125

Create equivalent expressions in the equation that all have equal bases.

5×2-4x=55

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

x2-4x=5

Move 5 to the left side of the equation by subtracting it from both sides.

x2-4x-5=0

Factor x2-4x-5 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -5 and whose sum is -4.

-5,1

Write the factored form using these integers.

(x-5)(x+1)=0

(x-5)(x+1)=0

Set x-5 equal to 0 and solve for x.

Set the factor equal to 0.

x-5=0

Add 5 to both sides of the equation.

x=5

x=5

Set x+1 equal to 0 and solve for x.

Set the factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

The solution is the result of x-5=0 and x+1=0.

x=5,-1

x=5,-1

Evaluate 5^(x^2)*5^(-4x)=3125