Question
Find the roots
Find the roots of the algebra expression
x1=2−210,x2=2+210
Alternative Form
x1≈−4.324555,x2≈8.324555
Evaluate
x2−4x−36
To find the roots of the expression,set the expression equal to 0
x2−4x−36=0
Substitute a=1,b=−4 and c=−36 into the quadratic formula x=2a−b±b2−4ac
x=24±(−4)2−4(−36)
Simplify the expression
More Steps
Evaluate
(−4)2−4(−36)
Multiply the numbers
More Steps
Evaluate
4(−36)
Multiplying or dividing an odd number of negative terms equals a negative
−4×36
Multiply the numbers
−144
(−4)2−(−144)
Rewrite the expression
42−(−144)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+144
Evaluate the power
16+144
Add the numbers
160
x=24±160
Simplify the radical expression
More Steps
Evaluate
160
Write the expression as a product where the root of one of the factors can be evaluated
16×10
Write the number in exponential form with the base of 4
42×10
The root of a product is equal to the product of the roots of each factor
42×10
Reduce the index of the radical and exponent with 2
410
x=24±410
Separate the equation into 2 possible cases
x=24+410x=24−410
Simplify the expression
More Steps
Evaluate
x=24+410
Divide the terms
More Steps
Evaluate
24+410
Rewrite the expression
22(2+210)
Reduce the fraction
2+210
x=2+210
x=2+210x=24−410
Simplify the expression
More Steps
Evaluate
x=24−410
Divide the terms
More Steps
Evaluate
24−410
Rewrite the expression
22(2−210)
Reduce the fraction
2−210
x=2−210
x=2+210x=2−210
Solution
x1=2−210,x2=2+210
Alternative Form
x1≈−4.324555,x2≈8.324555
Show Solution