Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=2−22,x2=2+22
Alternative Form
x1≈−0.828427,x2≈4.828427
Evaluate
x×x−4x−4=0
Multiply the terms
x2−4x−4=0
Substitute a=1,b=−4 and c=−4 into the quadratic formula x=2a−b±b2−4ac
x=24±(−4)2−4(−4)
Simplify the expression
More Steps

Evaluate
(−4)2−4(−4)
Multiply the numbers
More Steps

Evaluate
4(−4)
Multiplying or dividing an odd number of negative terms equals a negative
−4×4
Multiply the numbers
−16
(−4)2−(−16)
Rewrite the expression
42−(−16)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+16
Evaluate the power
16+16
Add the numbers
32
x=24±32
Simplify the radical expression
More Steps

Evaluate
32
Write the expression as a product where the root of one of the factors can be evaluated
16×2
Write the number in exponential form with the base of 4
42×2
The root of a product is equal to the product of the roots of each factor
42×2
Reduce the index of the radical and exponent with 2
42
x=24±42
Separate the equation into 2 possible cases
x=24+42x=24−42
Simplify the expression
More Steps

Evaluate
x=24+42
Divide the terms
More Steps

Evaluate
24+42
Rewrite the expression
22(2+22)
Reduce the fraction
2+22
x=2+22
x=2+22x=24−42
Simplify the expression
More Steps

Evaluate
x=24−42
Divide the terms
More Steps

Evaluate
24−42
Rewrite the expression
22(2−22)
Reduce the fraction
2−22
x=2−22
x=2+22x=2−22
Solution
x1=2−22,x2=2+22
Alternative Form
x1≈−0.828427,x2≈4.828427
Show Solution
