Question
Find the roots
Find the roots of the algebra expression
x1=64−1617,x2=64+1617
Alternative Form
x1≈−1.96969,x2≈129.96969
Evaluate
x2−128x−256
To find the roots of the expression,set the expression equal to 0
x2−128x−256=0
Substitute a=1,b=−128 and c=−256 into the quadratic formula x=2a−b±b2−4ac
x=2128±(−128)2−4(−256)
Simplify the expression
More Steps
Evaluate
(−128)2−4(−256)
Multiply the numbers
More Steps
Evaluate
4(−256)
Multiplying or dividing an odd number of negative terms equals a negative
−4×256
Multiply the numbers
−1024
(−128)2−(−1024)
Rewrite the expression
1282−(−1024)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1282+1024
Evaluate the power
16384+1024
Add the numbers
17408
x=2128±17408
Simplify the radical expression
More Steps
Evaluate
17408
Write the expression as a product where the root of one of the factors can be evaluated
1024×17
Write the number in exponential form with the base of 32
322×17
The root of a product is equal to the product of the roots of each factor
322×17
Reduce the index of the radical and exponent with 2
3217
x=2128±3217
Separate the equation into 2 possible cases
x=2128+3217x=2128−3217
Simplify the expression
More Steps
Evaluate
x=2128+3217
Divide the terms
More Steps
Evaluate
2128+3217
Rewrite the expression
22(64+1617)
Reduce the fraction
64+1617
x=64+1617
x=64+1617x=2128−3217
Simplify the expression
More Steps
Evaluate
x=2128−3217
Divide the terms
More Steps
Evaluate
2128−3217
Rewrite the expression
22(64−1617)
Reduce the fraction
64−1617
x=64−1617
x=64+1617x=64−1617
Solution
x1=64−1617,x2=64+1617
Alternative Form
x1≈−1.96969,x2≈129.96969
Show Solution