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

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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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

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