Solve Using the Square Root Property 1750=x(85-x)

Math
1750=x(85-x)
Rewrite the equation as x(85-x)=1750.
x(85-x)=1750
Simplify x(85-x).
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Simplify by multiplying through.
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Apply the distributive property.
x⋅85+x(-x)=1750
Reorder.
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Move 85 to the left of x.
85⋅x+x(-x)=1750
Rewrite using the commutative property of multiplication.
85⋅x-x⋅x=1750
85⋅x-x⋅x=1750
85⋅x-x⋅x=1750
Multiply x by x by adding the exponents.
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Move x.
85x-(x⋅x)=1750
Multiply x by x.
85x-x2=1750
85x-x2=1750
85x-x2=1750
Move 1750 to the left side of the equation by subtracting it from both sides.
85x-x2-1750=0
Factor the left side of the equation.
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Let u=x. Substitute u for all occurrences of x.
85u-u2-1750
Factor by grouping.
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Reorder terms.
-u2+85u-1750
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⋅-1750=1750 and whose sum is b=85.
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Factor 85 out of 85u.
-u2+85(u)-1750
Rewrite 85 as 35 plus 50
-u2+(35+50)u-1750
Apply the distributive property.
-u2+35u+50u-1750
-u2+35u+50u-1750
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(-u2+35u)+50u-1750
Factor out the greatest common factor (GCF) from each group.
u(-u+35)-50(-u+35)
u(-u+35)-50(-u+35)
Factor the polynomial by factoring out the greatest common factor, -u+35.
(-u+35)(u-50)
(-u+35)(u-50)
Replace all occurrences of u with x.
(-x+35)(x-50)
Replace the left side with the factored expression.
(-x+35)(x-50)=0
(-x+35)(x-50)=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+35=0
x-50=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
-x+35=0
Subtract 35 from both sides of the equation.
-x=-35
Multiply each term in -x=-35 by -1
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Multiply each term in -x=-35 by -1.
(-x)⋅-1=(-35)⋅-1
Multiply (-x)⋅-1.
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Multiply -1 by -1.
1x=(-35)⋅-1
Multiply x by 1.
x=(-35)⋅-1
x=(-35)⋅-1
Multiply -35 by -1.
x=35
x=35
x=35
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
x-50=0
Add 50 to both sides of the equation.
x=50
x=50
The final solution is all the values that make (-x+35)(x-50)=0 true.
x=35,50
Solve Using the Square Root Property 1750=x(85-x)

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