# Solve using the Square Root Property -3x(-(5x+3))-6x=75

-3x(-(5x+3))-6x=75
Simplify -3x(-(5x+3))-6x.
Simplify each term.
Apply the distributive property.
-3x(-(5x)-1⋅3)-6x=75
Multiply 5 by -1.
-3x(-5x-1⋅3)-6x=75
Multiply -1 by 3.
-3x(-5x-3)-6x=75
Apply the distributive property.
-3x(-5x)-3x⋅-3-6x=75
Multiply x by x.
-3⋅-5×2-3x⋅-3-6x=75
Multiply -3 by -3.
-3⋅-5×2+9x-6x=75
Multiply -3 by -5.
15×2+9x-6x=75
15×2+9x-6x=75
Subtract 6x from 9x.
15×2+3x=75
15×2+3x=75
Move 75 to the left side of the equation by subtracting it from both sides.
15×2+3x-75=0
Factor 3 out of 15×2+3x-75.
Factor 3 out of 15×2.
3(5×2)+3x-75=0
Factor 3 out of 3x.
3(5×2)+3(x)-75=0
Factor 3 out of -75.
3(5×2)+3x+3⋅-25=0
Factor 3 out of 3(5×2)+3x.
3(5×2+x)+3⋅-25=0
Factor 3 out of 3(5×2+x)+3⋅-25.
3(5×2+x-25)=0
3(5×2+x-25)=0
Divide each term by 3 and simplify.
Divide each term in 3(5×2+x-25)=0 by 3.
3(5×2+x-25)3=03
Cancel the common factor of 3.
Cancel the common factor.
3(5×2+x-25)3=03
Divide 5×2+x-25 by 1.
5×2+x-25=03
5×2+x-25=03
Divide 0 by 3.
5×2+x-25=0
5×2+x-25=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=1, and c=-25 into the quadratic formula and solve for x.
-1±12-4⋅(5⋅-25)2⋅5
Simplify.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(5⋅-25)2⋅5
Multiply 5 by -25.
x=-1±1-4⋅-1252⋅5
Multiply -4 by -125.
x=-1±1+5002⋅5
x=-1±5012⋅5
x=-1±5012⋅5
Multiply 2 by 5.
x=-1±50110
x=-1±50110
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(5⋅-25)2⋅5
Multiply 5 by -25.
x=-1±1-4⋅-1252⋅5
Multiply -4 by -125.
x=-1±1+5002⋅5
x=-1±5012⋅5
x=-1±5012⋅5
Multiply 2 by 5.
x=-1±50110
Change the ± to +.
x=-1+50110
Rewrite -1 as -1(1).
x=-1⋅1+50110
Factor -1 out of 501.
x=-1⋅1-1(-501)10
Factor -1 out of -1(1)-1(-501).
x=-1(1-501)10
Move the negative in front of the fraction.
x=-1-50110
x=-1-50110
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(5⋅-25)2⋅5
Multiply 5 by -25.
x=-1±1-4⋅-1252⋅5
Multiply -4 by -125.
x=-1±1+5002⋅5
x=-1±5012⋅5
x=-1±5012⋅5
Multiply 2 by 5.
x=-1±50110
Change the ± to -.
x=-1-50110
Rewrite -1 as -1(1).
x=-1⋅1-50110
Factor -1 out of -501.
x=-1⋅1-(501)10
Factor -1 out of -1(1)-(501).
x=-1(1+501)10
Move the negative in front of the fraction.
x=-1+50110
x=-1+50110
The final answer is the combination of both solutions.
x=-1-50110,-1+50110
The result can be shown in multiple forms.
Exact Form:
x=-1-50110,-1+50110
Decimal Form:
x=2.13830292…,-2.33830292…
Solve using the Square Root Property -3x(-(5x+3))-6x=75