Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=6−211,x2=6+211
Alternative Form
x1≈−0.63325,x2≈12.63325
Evaluate
x2−12x−8=0
Substitute a=1,b=−12 and c=−8 into the quadratic formula x=2a−b±b2−4ac
x=212±(−12)2−4(−8)
Simplify the expression
More Steps

Evaluate
(−12)2−4(−8)
Multiply the numbers
More Steps

Evaluate
4(−8)
Multiplying or dividing an odd number of negative terms equals a negative
−4×8
Multiply the numbers
−32
(−12)2−(−32)
Rewrite the expression
122−(−32)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+32
Evaluate the power
144+32
Add the numbers
176
x=212±176
Simplify the radical expression
More Steps

Evaluate
176
Write the expression as a product where the root of one of the factors can be evaluated
16×11
Write the number in exponential form with the base of 4
42×11
The root of a product is equal to the product of the roots of each factor
42×11
Reduce the index of the radical and exponent with 2
411
x=212±411
Separate the equation into 2 possible cases
x=212+411x=212−411
Simplify the expression
More Steps

Evaluate
x=212+411
Divide the terms
More Steps

Evaluate
212+411
Rewrite the expression
22(6+211)
Reduce the fraction
6+211
x=6+211
x=6+211x=212−411
Simplify the expression
More Steps

Evaluate
x=212−411
Divide the terms
More Steps

Evaluate
212−411
Rewrite the expression
22(6−211)
Reduce the fraction
6−211
x=6−211
x=6+211x=6−211
Solution
x1=6−211,x2=6+211
Alternative Form
x1≈−0.63325,x2≈12.63325
Show Solution
