# Solve Using the Square Root Property -3x(4x-9)+9x-43=2(x+9)

-3x(4x-9)+9x-43=2(x+9)
Simplify -3x(4x-9)+9x-43.
Simplify each term.
Apply the distributive property.
-3x(4x)-3x⋅-9+9x-43=2(x+9)
Multiply x by x.
-3⋅4×2-3x⋅-9+9x-43=2(x+9)
Multiply -9 by -3.
-3⋅4×2+27x+9x-43=2(x+9)
Multiply -3 by 4.
-12×2+27x+9x-43=2(x+9)
-12×2+27x+9x-43=2(x+9)
-12×2+36x-43=2(x+9)
-12×2+36x-43=2(x+9)
Simplify 2(x+9).
Apply the distributive property.
-12×2+36x-43=2x+2⋅9
Multiply 2 by 9.
-12×2+36x-43=2x+18
-12×2+36x-43=2x+18
Move all terms containing x to the left side of the equation.
Subtract 2x from both sides of the equation.
-12×2+36x-43-2x=18
Subtract 2x from 36x.
-12×2+34x-43=18
-12×2+34x-43=18
Move 18 to the left side of the equation by subtracting it from both sides.
-12×2+34x-43-18=0
Subtract 18 from -43.
-12×2+34x-61=0
Factor -1 out of -12×2+34x-61.
Factor -1 out of -12×2.
-(12×2)+34x-61=0
Factor -1 out of 34x.
-(12×2)-(-34x)-61=0
Rewrite -61 as -1(61).
-(12×2)-(-34x)-1⋅61=0
Factor -1 out of -(12×2)-(-34x).
-(12×2-34x)-1⋅61=0
Factor -1 out of -(12×2-34x)-1(61).
-(12×2-34x+61)=0
-(12×2-34x+61)=0
Multiply each term in -(12×2-34x+61)=0 by -1
Multiply each term in -(12×2-34x+61)=0 by -1.
-(12×2-34x+61)⋅-1=0⋅-1
Simplify -(12×2-34x+61)⋅-1.
Apply the distributive property.
(-(12×2)-(-34x)-1⋅61)⋅-1=0⋅-1
Simplify.
Multiply 12 by -1.
(-12×2-(-34x)-1⋅61)⋅-1=0⋅-1
Multiply -34 by -1.
(-12×2+34x-1⋅61)⋅-1=0⋅-1
Multiply -1 by 61.
(-12×2+34x-61)⋅-1=0⋅-1
(-12×2+34x-61)⋅-1=0⋅-1
Apply the distributive property.
-12×2⋅-1+34x⋅-1-61⋅-1=0⋅-1
Simplify.
Multiply -1 by -12.
12×2+34x⋅-1-61⋅-1=0⋅-1
Multiply -1 by 34.
12×2-34x-61⋅-1=0⋅-1
Multiply -61 by -1.
12×2-34x+61=0⋅-1
12×2-34x+61=0⋅-1
12×2-34x+61=0⋅-1
Multiply 0 by -1.
12×2-34x+61=0
12×2-34x+61=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=12, b=-34, and c=61 into the quadratic formula and solve for x.
34±(-34)2-4⋅(12⋅61)2⋅12
Simplify.
Simplify the numerator.
Raise -34 to the power of 2.
x=34±1156-4⋅(12⋅61)2⋅12
Multiply 12 by 61.
x=34±1156-4⋅7322⋅12
Multiply -4 by 732.
x=34±1156-29282⋅12
Subtract 2928 from 1156.
x=34±-17722⋅12
Rewrite -1772 as -1(1772).
x=34±-1⋅17722⋅12
Rewrite -1(1772) as -1⋅1772.
x=34±-1⋅17722⋅12
Rewrite -1 as i.
x=34±i⋅17722⋅12
Rewrite 1772 as 22⋅443.
Factor 4 out of 1772.
x=34±i⋅4(443)2⋅12
Rewrite 4 as 22.
x=34±i⋅22⋅4432⋅12
x=34±i⋅22⋅4432⋅12
Pull terms out from under the radical.
x=34±i⋅(2443)2⋅12
Move 2 to the left of i.
x=34±2i4432⋅12
x=34±2i4432⋅12
Multiply 2 by 12.
x=34±2i44324
Simplify 34±2i44324.
x=17±i44312
x=17±i44312
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -34 to the power of 2.
x=34±1156-4⋅(12⋅61)2⋅12
Multiply 12 by 61.
x=34±1156-4⋅7322⋅12
Multiply -4 by 732.
x=34±1156-29282⋅12
Subtract 2928 from 1156.
x=34±-17722⋅12
Rewrite -1772 as -1(1772).
x=34±-1⋅17722⋅12
Rewrite -1(1772) as -1⋅1772.
x=34±-1⋅17722⋅12
Rewrite -1 as i.
x=34±i⋅17722⋅12
Rewrite 1772 as 22⋅443.
Factor 4 out of 1772.
x=34±i⋅4(443)2⋅12
Rewrite 4 as 22.
x=34±i⋅22⋅4432⋅12
x=34±i⋅22⋅4432⋅12
Pull terms out from under the radical.
x=34±i⋅(2443)2⋅12
Move 2 to the left of i.
x=34±2i4432⋅12
x=34±2i4432⋅12
Multiply 2 by 12.
x=34±2i44324
Simplify 34±2i44324.
x=17±i44312
Change the ± to +.
x=17+i44312
x=17+i44312
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -34 to the power of 2.
x=34±1156-4⋅(12⋅61)2⋅12
Multiply 12 by 61.
x=34±1156-4⋅7322⋅12
Multiply -4 by 732.
x=34±1156-29282⋅12
Subtract 2928 from 1156.
x=34±-17722⋅12
Rewrite -1772 as -1(1772).
x=34±-1⋅17722⋅12
Rewrite -1(1772) as -1⋅1772.
x=34±-1⋅17722⋅12
Rewrite -1 as i.
x=34±i⋅17722⋅12
Rewrite 1772 as 22⋅443.
Factor 4 out of 1772.
x=34±i⋅4(443)2⋅12
Rewrite 4 as 22.
x=34±i⋅22⋅4432⋅12
x=34±i⋅22⋅4432⋅12
Pull terms out from under the radical.
x=34±i⋅(2443)2⋅12
Move 2 to the left of i.
x=34±2i4432⋅12
x=34±2i4432⋅12
Multiply 2 by 12.
x=34±2i44324
Simplify 34±2i44324.
x=17±i44312
Change the ± to -.
x=17-i44312
x=17-i44312
The final answer is the combination of both solutions.
x=17+i44312,17-i44312
Solve Using the Square Root Property -3x(4x-9)+9x-43=2(x+9)