Question
Find the roots
x1=3−13,x2=3+13
Alternative Form
x1≈−0.605551,x2≈6.605551
Evaluate
x2−6x−4
To find the roots of the expression,set the expression equal to 0
x2−6x−4=0
Substitute a=1,b=−6 and c=−4 into the quadratic formula x=2a−b±b2−4ac
x=26±(−6)2−4(−4)
Simplify the expression
More Steps

Evaluate
(−6)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
(−6)2−(−16)
Rewrite the expression
62−(−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
62+16
Evaluate the power
36+16
Add the numbers
52
x=26±52
Simplify the radical expression
More Steps

Evaluate
52
Write the expression as a product where the root of one of the factors can be evaluated
4×13
Write the number in exponential form with the base of 2
22×13
The root of a product is equal to the product of the roots of each factor
22×13
Reduce the index of the radical and exponent with 2
213
x=26±213
Separate the equation into 2 possible cases
x=26+213x=26−213
Simplify the expression
More Steps

Evaluate
x=26+213
Divide the terms
More Steps

Evaluate
26+213
Rewrite the expression
22(3+13)
Reduce the fraction
3+13
x=3+13
x=3+13x=26−213
Simplify the expression
More Steps

Evaluate
x=26−213
Divide the terms
More Steps

Evaluate
26−213
Rewrite the expression
22(3−13)
Reduce the fraction
3−13
x=3−13
x=3+13x=3−13
Solution
x1=3−13,x2=3+13
Alternative Form
x1≈−0.605551,x2≈6.605551
Show Solution
