95x-x2=94

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

95x-x2=94

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

5x-x2=4

Move 4 to the left side of the equation by subtracting it from both sides.

5x-x2-4=0

Factor the left side of the equation.

Let u=x. Substitute u for all occurrences of x.

5u-u2-4

Factor by grouping.

Reorder terms.

-u2+5u-4

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅-4=4 and whose sum is b=5.

Factor 5 out of 5u.

-u2+5(u)-4

Rewrite 5 as 1 plus 4

-u2+(1+4)u-4

Apply the distributive property.

-u2+1u+4u-4

Multiply u by 1.

-u2+u+4u-4

-u2+u+4u-4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-u2+u)+4u-4

Factor out the greatest common factor (GCF) from each group.

u(-u+1)-4(-u+1)

u(-u+1)-4(-u+1)

Factor the polynomial by factoring out the greatest common factor, -u+1.

(-u+1)(u-4)

(-u+1)(u-4)

Replace all occurrences of u with x.

(-x+1)(x-4)

Replace the left side with the factored expression.

(-x+1)(x-4)=0

(-x+1)(x-4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

-x+1=0

x-4=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

-x+1=0

Subtract 1 from both sides of the equation.

-x=-1

Multiply each term in -x=-1 by -1

Multiply each term in -x=-1 by -1.

(-x)⋅-1=(-1)⋅-1

Multiply (-x)⋅-1.

Multiply -1 by -1.

1x=(-1)⋅-1

Multiply x by 1.

x=(-1)⋅-1

x=(-1)⋅-1

Multiply -1 by -1.

x=1

x=1

x=1

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

The final solution is all the values that make (-x+1)(x-4)=0 true.

x=1,4

x=1,4

Solve using the Square Root Property 9^(5x-x^2)=9^4