x2-76x+13=0

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

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 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 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

Add 7 and 1.

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 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