1750=x(85-x)

Rewrite the equation as x(85-x)=1750.

x(85-x)=1750

Simplify by multiplying through.

Apply the distributive property.

x⋅85+x(-x)=1750

Reorder.

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.

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

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

85u-u2-1750

Factor by grouping.

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.

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.

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.

-x+35=0

Subtract 35 from both sides of the equation.

-x=-35

Multiply each term in -x=-35 by -1

Multiply each term in -x=-35 by -1.

(-x)⋅-1=(-35)⋅-1

Multiply (-x)⋅-1.

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.

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)