Question
Find the roots
x1=−2−2i,x2=−2+2i
Evaluate
x2+4x+8
To find the roots of the expression,set the expression equal to 0
x2+4x+8=0
Substitute a=1,b=4 and c=8 into the quadratic formula x=2a−b±b2−4ac
x=2−4±42−4×8
Simplify the expression
More Steps

Evaluate
42−4×8
Multiply the numbers
42−32
Evaluate the power
16−32
Subtract the numbers
−16
x=2−4±−16
Simplify the radical expression
More Steps

Evaluate
−16
Evaluate the power
16×−1
Evaluate the power
16×i
Evaluate the square root
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Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
4i
x=2−4±4i
Separate the equation into 2 possible cases
x=2−4+4ix=2−4−4i
Simplify the expression
More Steps

Evaluate
x=2−4+4i
Divide the terms
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Evaluate
2−4+4i
Rewrite the expression
22(−2+2i)
Reduce the fraction
−2+2i
x=−2+2i
x=−2+2ix=2−4−4i
Simplify the expression
More Steps

Evaluate
x=2−4−4i
Divide the terms
More Steps

Evaluate
2−4−4i
Rewrite the expression
22(−2−2i)
Reduce the fraction
−2−2i
x=−2−2i
x=−2+2ix=−2−2i
Solution
x1=−2−2i,x2=−2+2i
Show Solution
