Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=3−32,x2=3+32
Alternative Form
x1≈−1.242641,x2≈7.242641
Evaluate
x2−6x−9=0
Substitute a=1,b=−6 and c=−9 into the quadratic formula x=2a−b±b2−4ac
x=26±(−6)2−4(−9)
Simplify the expression
More Steps

Evaluate
(−6)2−4(−9)
Multiply the numbers
More Steps

Evaluate
4(−9)
Multiplying or dividing an odd number of negative terms equals a negative
−4×9
Multiply the numbers
−36
(−6)2−(−36)
Rewrite the expression
62−(−36)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
62+36
Evaluate the power
36+36
Add the numbers
72
x=26±72
Simplify the radical expression
More Steps

Evaluate
72
Write the expression as a product where the root of one of the factors can be evaluated
36×2
Write the number in exponential form with the base of 6
62×2
The root of a product is equal to the product of the roots of each factor
62×2
Reduce the index of the radical and exponent with 2
62
x=26±62
Separate the equation into 2 possible cases
x=26+62x=26−62
Simplify the expression
More Steps

Evaluate
x=26+62
Divide the terms
More Steps

Evaluate
26+62
Rewrite the expression
22(3+32)
Reduce the fraction
3+32
x=3+32
x=3+32x=26−62
Simplify the expression
More Steps

Evaluate
x=26−62
Divide the terms
More Steps

Evaluate
26−62
Rewrite the expression
22(3−32)
Reduce the fraction
3−32
x=3−32
x=3+32x=3−32
Solution
x1=3−32,x2=3+32
Alternative Form
x1≈−1.242641,x2≈7.242641
Show Solution
