# Solve using the Square Root Property -(5z(10z+2))=2+(4z+3)

-(5z(10z+2))=2+(4z+3)
Simplify -(5z(10z+2)).
Apply the distributive property.
-(5z(10z)+5z⋅2)=2+4z+3
Simplify the expression.
Multiply z by z.
-(5⋅10z2+5z⋅2)=2+4z+3
Multiply 2 by 5.
-(5⋅10z2+10z)=2+4z+3
Multiply 5 by 10.
-(50z2+10z)=2+4z+3
-(50z2+10z)=2+4z+3
Apply the distributive property.
-(50z2)-(10z)=2+4z+3
Multiply.
Multiply 50 by -1.
-50z2-(10z)=2+4z+3
Multiply 10 by -1.
-50z2-10z=2+4z+3
-50z2-10z=2+4z+3
-50z2-10z=2+4z+3
-50z2-10z=4z+5
Move all terms containing z to the left side of the equation.
Subtract 4z from both sides of the equation.
-50z2-10z-4z=5
Subtract 4z from -10z.
-50z2-14z=5
-50z2-14z=5
Move 5 to the left side of the equation by subtracting it from both sides.
-50z2-14z-5=0
Factor -1 out of -50z2-14z-5.
Factor -1 out of -50z2.
-(50z2)-14z-5=0
Factor -1 out of -14z.
-(50z2)-(14z)-5=0
Rewrite -5 as -1(5).
-(50z2)-(14z)-1⋅5=0
Factor -1 out of -(50z2)-(14z).
-(50z2+14z)-1⋅5=0
Factor -1 out of -(50z2+14z)-1(5).
-(50z2+14z+5)=0
-(50z2+14z+5)=0
Multiply each term in -(50z2+14z+5)=0 by -1
Multiply each term in -(50z2+14z+5)=0 by -1.
-(50z2+14z+5)⋅-1=0⋅-1
Simplify -(50z2+14z+5)⋅-1.
Apply the distributive property.
(-(50z2)-(14z)-1⋅5)⋅-1=0⋅-1
Simplify.
Multiply 50 by -1.
(-50z2-(14z)-1⋅5)⋅-1=0⋅-1
Multiply 14 by -1.
(-50z2-14z-1⋅5)⋅-1=0⋅-1
Multiply -1 by 5.
(-50z2-14z-5)⋅-1=0⋅-1
(-50z2-14z-5)⋅-1=0⋅-1
Apply the distributive property.
-50z2⋅-1-14z⋅-1-5⋅-1=0⋅-1
Simplify.
Multiply -1 by -50.
50z2-14z⋅-1-5⋅-1=0⋅-1
Multiply -1 by -14.
50z2+14z-5⋅-1=0⋅-1
Multiply -5 by -1.
50z2+14z+5=0⋅-1
50z2+14z+5=0⋅-1
50z2+14z+5=0⋅-1
Multiply 0 by -1.
50z2+14z+5=0
50z2+14z+5=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=50, b=14, and c=5 into the quadratic formula and solve for z.
-14±142-4⋅(50⋅5)2⋅50
Simplify.
Simplify the numerator.
Raise 14 to the power of 2.
z=-14±196-4⋅(50⋅5)2⋅50
Multiply 50 by 5.
z=-14±196-4⋅2502⋅50
Multiply -4 by 250.
z=-14±196-10002⋅50
Subtract 1000 from 196.
z=-14±-8042⋅50
Rewrite -804 as -1(804).
z=-14±-1⋅8042⋅50
Rewrite -1(804) as -1⋅804.
z=-14±-1⋅8042⋅50
Rewrite -1 as i.
z=-14±i⋅8042⋅50
Rewrite 804 as 22⋅201.
Factor 4 out of 804.
z=-14±i⋅4(201)2⋅50
Rewrite 4 as 22.
z=-14±i⋅22⋅2012⋅50
z=-14±i⋅22⋅2012⋅50
Pull terms out from under the radical.
z=-14±i⋅(2201)2⋅50
Move 2 to the left of i.
z=-14±2i2012⋅50
z=-14±2i2012⋅50
Multiply 2 by 50.
z=-14±2i201100
Simplify -14±2i201100.
z=-7±i20150
z=-7±i20150
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 14 to the power of 2.
z=-14±196-4⋅(50⋅5)2⋅50
Multiply 50 by 5.
z=-14±196-4⋅2502⋅50
Multiply -4 by 250.
z=-14±196-10002⋅50
Subtract 1000 from 196.
z=-14±-8042⋅50
Rewrite -804 as -1(804).
z=-14±-1⋅8042⋅50
Rewrite -1(804) as -1⋅804.
z=-14±-1⋅8042⋅50
Rewrite -1 as i.
z=-14±i⋅8042⋅50
Rewrite 804 as 22⋅201.
Factor 4 out of 804.
z=-14±i⋅4(201)2⋅50
Rewrite 4 as 22.
z=-14±i⋅22⋅2012⋅50
z=-14±i⋅22⋅2012⋅50
Pull terms out from under the radical.
z=-14±i⋅(2201)2⋅50
Move 2 to the left of i.
z=-14±2i2012⋅50
z=-14±2i2012⋅50
Multiply 2 by 50.
z=-14±2i201100
Simplify -14±2i201100.
z=-7±i20150
Change the ± to +.
z=-7+i20150
Rewrite -7 as -1(7).
z=-1⋅7+i20150
Factor -1 out of i201.
z=-1⋅7-(-i201)50
Factor -1 out of -1(7)-(-i201).
z=-1(7-i201)50
Move the negative in front of the fraction.
z=-7-i20150
z=-7-i20150
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 14 to the power of 2.
z=-14±196-4⋅(50⋅5)2⋅50
Multiply 50 by 5.
z=-14±196-4⋅2502⋅50
Multiply -4 by 250.
z=-14±196-10002⋅50
Subtract 1000 from 196.
z=-14±-8042⋅50
Rewrite -804 as -1(804).
z=-14±-1⋅8042⋅50
Rewrite -1(804) as -1⋅804.
z=-14±-1⋅8042⋅50
Rewrite -1 as i.
z=-14±i⋅8042⋅50
Rewrite 804 as 22⋅201.
Factor 4 out of 804.
z=-14±i⋅4(201)2⋅50
Rewrite 4 as 22.
z=-14±i⋅22⋅2012⋅50
z=-14±i⋅22⋅2012⋅50
Pull terms out from under the radical.
z=-14±i⋅(2201)2⋅50
Move 2 to the left of i.
z=-14±2i2012⋅50
z=-14±2i2012⋅50
Multiply 2 by 50.
z=-14±2i201100
Simplify -14±2i201100.
z=-7±i20150
Change the ± to -.
z=-7-i20150
Rewrite -7 as -1(7).
z=-1⋅7-i20150
Factor -1 out of -i201.
z=-1⋅7-(i201)50
Factor -1 out of -1(7)-(i201).
z=-1(7+i201)50
Move the negative in front of the fraction.
z=-7+i20150
z=-7+i20150
The final answer is the combination of both solutions.
z=-7-i20150,-7+i20150
Solve using the Square Root Property -(5z(10z+2))=2+(4z+3)