# Solve Using the Square Root Property 0.06x(12720-x)=12 0.06x(12720-x)=12
Divide each term by 0.06 and simplify.
Divide each term in 0.06x(12720-x)=12 by 0.06.
0.06x(12720-x)0.06=120.06
Cancel the common factor of 0.06.
12720x-x2=120.06
Divide 12 by 0.06.
12720x-x2=200
12720x-x2=200
Move 200 to the left side of the equation by subtracting it from both sides.
12720x-x2-200=0
Factor -1 out of 12720x-x2-200.
Reorder 12720x and -x2.
-x2+12720x-200=0
Factor -1 out of -x2.
-(x2)+12720x-200=0
Factor -1 out of 12720x.
-(x2)-(-12720x)-200=0
Rewrite -200 as -1(200).
-(x2)-(-12720x)-1⋅200=0
Factor -1 out of -(x2)-(-12720x).
-(x2-12720x)-1⋅200=0
Factor -1 out of -(x2-12720x)-1(200).
-(x2-12720x+200)=0
-(x2-12720x+200)=0
Multiply each term in -(x2-12720x+200)=0 by -1
Multiply each term in -(x2-12720x+200)=0 by -1.
-(x2-12720x+200)⋅-1=0⋅-1
Simplify -(x2-12720x+200)⋅-1.
Apply the distributive property.
(-x2-(-12720x)-1⋅200)⋅-1=0⋅-1
Simplify.
Multiply -12720 by -1.
(-x2+12720x-1⋅200)⋅-1=0⋅-1
Multiply -1 by 200.
(-x2+12720x-200)⋅-1=0⋅-1
(-x2+12720x-200)⋅-1=0⋅-1
Apply the distributive property.
-x2⋅-1+12720x⋅-1-200⋅-1=0⋅-1
Simplify.
Multiply -x2⋅-1.
Multiply -1 by -1.
1×2+12720x⋅-1-200⋅-1=0⋅-1
Multiply x2 by 1.
x2+12720x⋅-1-200⋅-1=0⋅-1
x2+12720x⋅-1-200⋅-1=0⋅-1
Multiply -1 by 12720.
x2-12720x-200⋅-1=0⋅-1
Multiply -200 by -1.
x2-12720x+200=0⋅-1
x2-12720x+200=0⋅-1
x2-12720x+200=0⋅-1
Multiply 0 by -1.
x2-12720x+200=0
x2-12720x+200=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-12720, and c=200 into the quadratic formula and solve for x.
12720±(-12720)2-4⋅(1⋅200)2⋅1
Simplify.
Simplify the numerator.
Raise -12720 to the power of 2.
x=12720±161798400-4⋅(1⋅200)2⋅1
Multiply 200 by 1.
x=12720±161798400-4⋅2002⋅1
Multiply -4 by 200.
x=12720±161798400-8002⋅1
Subtract 800 from 161798400.
x=12720±1617976002⋅1
Rewrite 161797600 as 202⋅404494.
Factor 400 out of 161797600.
x=12720±400(404494)2⋅1
Rewrite 400 as 202.
x=12720±202⋅4044942⋅1
x=12720±202⋅4044942⋅1
Pull terms out from under the radical.
x=12720±204044942⋅1
x=12720±204044942⋅1
Multiply 2 by 1.
x=12720±204044942
Simplify 12720±204044942.
x=6360±10404494
x=6360±10404494
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -12720 to the power of 2.
x=12720±161798400-4⋅(1⋅200)2⋅1
Multiply 200 by 1.
x=12720±161798400-4⋅2002⋅1
Multiply -4 by 200.
x=12720±161798400-8002⋅1
Subtract 800 from 161798400.
x=12720±1617976002⋅1
Rewrite 161797600 as 202⋅404494.
Factor 400 out of 161797600.
x=12720±400(404494)2⋅1
Rewrite 400 as 202.
x=12720±202⋅4044942⋅1
x=12720±202⋅4044942⋅1
Pull terms out from under the radical.
x=12720±204044942⋅1
x=12720±204044942⋅1
Multiply 2 by 1.
x=12720±204044942
Simplify 12720±204044942.
x=6360±10404494
Change the ± to +.
x=6360+10404494
x=6360+10404494
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -12720 to the power of 2.
x=12720±161798400-4⋅(1⋅200)2⋅1
Multiply 200 by 1.
x=12720±161798400-4⋅2002⋅1
Multiply -4 by 200.
x=12720±161798400-8002⋅1
Subtract 800 from 161798400.
x=12720±1617976002⋅1
Rewrite 161797600 as 202⋅404494.
Factor 400 out of 161797600.
x=12720±400(404494)2⋅1
Rewrite 400 as 202.
x=12720±202⋅4044942⋅1
x=12720±202⋅4044942⋅1
Pull terms out from under the radical.
x=12720±204044942⋅1
x=12720±204044942⋅1
Multiply 2 by 1.
x=12720±204044942
Simplify 12720±204044942.
x=6360±10404494
Change the ± to -.
x=6360-10404494
x=6360-10404494
The final answer is the combination of both solutions.
x=6360+10404494,6360-10404494
The result can be shown in multiple forms.
Exact Form:
x=6360+10404494,6360-10404494
Decimal Form:
x=12719.98427671…,0.01572328…
Solve Using the Square Root Property 0.06x(12720-x)=12     