Solve using the Square Root Property x^2+4x+29=0

Math
x2+4x+29=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=4, and c=29 into the quadratic formula and solve for x.
-4±42-4⋅(1⋅29)2⋅1
Simplify.
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Simplify the numerator.
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Raise 4 to the power of 2.
x=-4±16-4⋅(1⋅29)2⋅1
Multiply 29 by 1.
x=-4±16-4⋅292⋅1
Multiply -4 by 29.
x=-4±16-1162⋅1
Subtract 116 from 16.
x=-4±-1002⋅1
Rewrite -100 as -1(100).
x=-4±-1⋅1002⋅1
Rewrite -1(100) as -1⋅100.
x=-4±-1⋅1002⋅1
Rewrite -1 as i.
x=-4±i⋅1002⋅1
Rewrite 100 as 102.
x=-4±i⋅1022⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=-4±i⋅102⋅1
Move 10 to the left of i.
x=-4±10i2⋅1
x=-4±10i2⋅1
Multiply 2 by 1.
x=-4±10i2
Simplify -4±10i2.
x=-2±5i
x=-2±5i
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise 4 to the power of 2.
x=-4±16-4⋅(1⋅29)2⋅1
Multiply 29 by 1.
x=-4±16-4⋅292⋅1
Multiply -4 by 29.
x=-4±16-1162⋅1
Subtract 116 from 16.
x=-4±-1002⋅1
Rewrite -100 as -1(100).
x=-4±-1⋅1002⋅1
Rewrite -1(100) as -1⋅100.
x=-4±-1⋅1002⋅1
Rewrite -1 as i.
x=-4±i⋅1002⋅1
Rewrite 100 as 102.
x=-4±i⋅1022⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=-4±i⋅102⋅1
Move 10 to the left of i.
x=-4±10i2⋅1
x=-4±10i2⋅1
Multiply 2 by 1.
x=-4±10i2
Simplify -4±10i2.
x=-2±5i
Change the ± to +.
x=-2+5i
x=-2+5i
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise 4 to the power of 2.
x=-4±16-4⋅(1⋅29)2⋅1
Multiply 29 by 1.
x=-4±16-4⋅292⋅1
Multiply -4 by 29.
x=-4±16-1162⋅1
Subtract 116 from 16.
x=-4±-1002⋅1
Rewrite -100 as -1(100).
x=-4±-1⋅1002⋅1
Rewrite -1(100) as -1⋅100.
x=-4±-1⋅1002⋅1
Rewrite -1 as i.
x=-4±i⋅1002⋅1
Rewrite 100 as 102.
x=-4±i⋅1022⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=-4±i⋅102⋅1
Move 10 to the left of i.
x=-4±10i2⋅1
x=-4±10i2⋅1
Multiply 2 by 1.
x=-4±10i2
Simplify -4±10i2.
x=-2±5i
Change the ± to -.
x=-2-5i
x=-2-5i
The final answer is the combination of both solutions.
x=-2+5i,-2-5i
Solve using the Square Root Property x^2+4x+29=0

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