9y2-36y+37=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=9, b=-36, and c=37 into the quadratic formula and solve for y.

36±(-36)2-4⋅(9⋅37)2⋅9

Simplify the numerator.

Raise -36 to the power of 2.

y=36±1296-4⋅(9⋅37)2⋅9

Multiply 9 by 37.

y=36±1296-4⋅3332⋅9

Multiply -4 by 333.

y=36±1296-13322⋅9

Subtract 1332 from 1296.

y=36±-362⋅9

Rewrite -36 as -1(36).

y=36±-1⋅362⋅9

Rewrite -1(36) as -1⋅36.

y=36±-1⋅362⋅9

Rewrite -1 as i.

y=36±i⋅362⋅9

Rewrite 36 as 62.

y=36±i⋅622⋅9

Pull terms out from under the radical, assuming positive real numbers.

y=36±i⋅62⋅9

Move 6 to the left of i.

y=36±6i2⋅9

y=36±6i2⋅9

Multiply 2 by 9.

y=36±6i18

Simplify 36±6i18.

y=6±i3

y=6±i3

Simplify the numerator.

Raise -36 to the power of 2.

y=36±1296-4⋅(9⋅37)2⋅9

Multiply 9 by 37.

y=36±1296-4⋅3332⋅9

Multiply -4 by 333.

y=36±1296-13322⋅9

Subtract 1332 from 1296.

y=36±-362⋅9

Rewrite -36 as -1(36).

y=36±-1⋅362⋅9

Rewrite -1(36) as -1⋅36.

y=36±-1⋅362⋅9

Rewrite -1 as i.

y=36±i⋅362⋅9

Rewrite 36 as 62.

y=36±i⋅622⋅9

Pull terms out from under the radical, assuming positive real numbers.

y=36±i⋅62⋅9

Move 6 to the left of i.

y=36±6i2⋅9

y=36±6i2⋅9

Multiply 2 by 9.

y=36±6i18

Simplify 36±6i18.

y=6±i3

Change the ± to +.

y=6+i3

Split the fraction 6+i3 into two fractions.

y=63+i3

Divide 6 by 3.

y=2+i3

y=2+i3

Simplify the numerator.

Raise -36 to the power of 2.

y=36±1296-4⋅(9⋅37)2⋅9

Multiply 9 by 37.

y=36±1296-4⋅3332⋅9

Multiply -4 by 333.

y=36±1296-13322⋅9

Subtract 1332 from 1296.

y=36±-362⋅9

Rewrite -36 as -1(36).

y=36±-1⋅362⋅9

Rewrite -1(36) as -1⋅36.

y=36±-1⋅362⋅9

Rewrite -1 as i.

y=36±i⋅362⋅9

Rewrite 36 as 62.

y=36±i⋅622⋅9

Pull terms out from under the radical, assuming positive real numbers.

y=36±i⋅62⋅9

Move 6 to the left of i.

y=36±6i2⋅9

y=36±6i2⋅9

Multiply 2 by 9.

y=36±6i18

Simplify 36±6i18.

y=6±i3

Change the ± to -.

y=6-i3

Split the fraction 6-i3 into two fractions.

y=63+-i3

Simplify each term.

Divide 6 by 3.

y=2+-i3

Move the negative in front of the fraction.

y=2-i3

y=2-i3

y=2-i3

The final answer is the combination of both solutions.

y=2+i3,2-i3

Solve using the Square Root Property 9y^2-36y+37=0