# Solve Using the Square Root Property x^2-7/6x+1/3=0

x2-76x+13=0
Simplify each term.
Combine x and 76.
x2-x⋅76+13=0
Move 7 to the left of x.
x2-7×6+13=0
x2-7×6+13=0
Multiply through by the least common denominator 6, then simplify.
Apply the distributive property.
6×2+6(-7×6)+6(13)=0
Simplify.
Cancel the common factor of 6.
Move the leading negative in -7×6 into the numerator.
6×2+6(-7×6)+6(13)=0
Cancel the common factor.
6×2+6(-7×6)+6(13)=0
Rewrite the expression.
6×2-7x+6(13)=0
6×2-7x+6(13)=0
Cancel the common factor of 3.
Factor 3 out of 6.
6×2-7x+3(2)(13)=0
Cancel the common factor.
6×2-7x+3⋅(2(13))=0
Rewrite the expression.
6×2-7x+2=0
6×2-7x+2=0
6×2-7x+2=0
6×2-7x+2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=6, b=-7, and c=2 into the quadratic formula and solve for x.
7±(-7)2-4⋅(6⋅2)2⋅6
Simplify.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(6⋅2)2⋅6
Multiply 6 by 2.
x=7±49-4⋅122⋅6
Multiply -4 by 12.
x=7±49-482⋅6
Subtract 48 from 49.
x=7±12⋅6
Any root of 1 is 1.
x=7±12⋅6
x=7±12⋅6
Multiply 2 by 6.
x=7±112
x=7±112
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(6⋅2)2⋅6
Multiply 6 by 2.
x=7±49-4⋅122⋅6
Multiply -4 by 12.
x=7±49-482⋅6
Subtract 48 from 49.
x=7±12⋅6
Any root of 1 is 1.
x=7±12⋅6
x=7±12⋅6
Multiply 2 by 6.
x=7±112
Change the ± to +.
x=7+112
x=812
Cancel the common factor of 8 and 12.
Factor 4 out of 8.
x=4(2)12
Cancel the common factors.
Factor 4 out of 12.
x=4⋅24⋅3
Cancel the common factor.
x=4⋅24⋅3
Rewrite the expression.
x=23
x=23
x=23
x=23
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(6⋅2)2⋅6
Multiply 6 by 2.
x=7±49-4⋅122⋅6
Multiply -4 by 12.
x=7±49-482⋅6
Subtract 48 from 49.
x=7±12⋅6
Any root of 1 is 1.
x=7±12⋅6
x=7±12⋅6
Multiply 2 by 6.
x=7±112
Change the ± to -.
x=7-112
Subtract 1 from 7.
x=612
Cancel the common factor of 6 and 12.
Factor 6 out of 6.
x=6(1)12
Cancel the common factors.
Factor 6 out of 12.
x=6⋅16⋅2
Cancel the common factor.
x=6⋅16⋅2
Rewrite the expression.
x=12
x=12
x=12
x=12
The final answer is the combination of both solutions.
x=23,12
Solve Using the Square Root Property x^2-7/6x+1/3=0