Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
a1=22−5,a2=22+5
Alternative Form
a1≈−0.118034,a2≈2.118034
Evaluate
4a2−8a−1=0
Substitute a=4,b=−8 and c=−1 into the quadratic formula a=2a−b±b2−4ac
a=2×48±(−8)2−4×4(−1)
Simplify the expression
a=88±(−8)2−4×4(−1)
Simplify the expression
More Steps

Evaluate
(−8)2−4×4(−1)
Multiply
More Steps

Multiply the terms
4×4(−1)
Any expression multiplied by 1 remains the same
−4×4
Multiply the terms
−16
(−8)2−(−16)
Rewrite the expression
82−(−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
82+16
Evaluate the power
64+16
Add the numbers
80
a=88±80
Simplify the radical expression
More Steps

Evaluate
80
Write the expression as a product where the root of one of the factors can be evaluated
16×5
Write the number in exponential form with the base of 4
42×5
The root of a product is equal to the product of the roots of each factor
42×5
Reduce the index of the radical and exponent with 2
45
a=88±45
Separate the equation into 2 possible cases
a=88+45a=88−45
Simplify the expression
More Steps

Evaluate
a=88+45
Divide the terms
More Steps

Evaluate
88+45
Rewrite the expression
84(2+5)
Cancel out the common factor 4
22+5
a=22+5
a=22+5a=88−45
Simplify the expression
More Steps

Evaluate
a=88−45
Divide the terms
More Steps

Evaluate
88−45
Rewrite the expression
84(2−5)
Cancel out the common factor 4
22−5
a=22−5
a=22+5a=22−5
Solution
a1=22−5,a2=22+5
Alternative Form
a1≈−0.118034,a2≈2.118034
Show Solution
