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

Math
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
Solve for x.
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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.
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Let u=x. Substitute u for all occurrences of x.
5u-u2-4
Factor by grouping.
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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.
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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.
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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.
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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
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Multiply each term in -x=-1 by -1.
(-x)⋅-1=(-1)⋅-1
Multiply (-x)⋅-1.
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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.
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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

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