Solve Using the Square Root Property x^2-12x+72=0

Math
x2-12x+72=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-12, and c=72 into the quadratic formula and solve for x.
12±(-12)2-4⋅(1⋅72)2⋅1
Simplify.
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Simplify the numerator.
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Raise -12 to the power of 2.
x=12±144-4⋅(1⋅72)2⋅1
Multiply 72 by 1.
x=12±144-4⋅722⋅1
Multiply -4 by 72.
x=12±144-2882⋅1
Subtract 288 from 144.
x=12±-1442⋅1
Rewrite -144 as -1(144).
x=12±-1⋅1442⋅1
Rewrite -1(144) as -1⋅144.
x=12±-1⋅1442⋅1
Rewrite -1 as i.
x=12±i⋅1442⋅1
Rewrite 144 as 122.
x=12±i⋅1222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=12±i⋅122⋅1
Move 12 to the left of i.
x=12±12i2⋅1
x=12±12i2⋅1
Multiply 2 by 1.
x=12±12i2
Simplify 12±12i2.
x=6±6i
x=6±6i
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -12 to the power of 2.
x=12±144-4⋅(1⋅72)2⋅1
Multiply 72 by 1.
x=12±144-4⋅722⋅1
Multiply -4 by 72.
x=12±144-2882⋅1
Subtract 288 from 144.
x=12±-1442⋅1
Rewrite -144 as -1(144).
x=12±-1⋅1442⋅1
Rewrite -1(144) as -1⋅144.
x=12±-1⋅1442⋅1
Rewrite -1 as i.
x=12±i⋅1442⋅1
Rewrite 144 as 122.
x=12±i⋅1222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=12±i⋅122⋅1
Move 12 to the left of i.
x=12±12i2⋅1
x=12±12i2⋅1
Multiply 2 by 1.
x=12±12i2
Simplify 12±12i2.
x=6±6i
Change the ± to +.
x=6+6i
x=6+6i
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -12 to the power of 2.
x=12±144-4⋅(1⋅72)2⋅1
Multiply 72 by 1.
x=12±144-4⋅722⋅1
Multiply -4 by 72.
x=12±144-2882⋅1
Subtract 288 from 144.
x=12±-1442⋅1
Rewrite -144 as -1(144).
x=12±-1⋅1442⋅1
Rewrite -1(144) as -1⋅144.
x=12±-1⋅1442⋅1
Rewrite -1 as i.
x=12±i⋅1442⋅1
Rewrite 144 as 122.
x=12±i⋅1222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=12±i⋅122⋅1
Move 12 to the left of i.
x=12±12i2⋅1
x=12±12i2⋅1
Multiply 2 by 1.
x=12±12i2
Simplify 12±12i2.
x=6±6i
Change the ± to -.
x=6-6i
x=6-6i
The final answer is the combination of both solutions.
x=6+6i,6-6i
Solve Using the Square Root Property x^2-12x+72=0

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