Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=1−27,x2=1+27
Alternative Form
x1≈−4.291503,x2≈6.291503
Evaluate
x2−2x−27
To find the roots of the expression,set the expression equal to 0
x2−2x−27=0
Substitute a=1,b=−2 and c=−27 into the quadratic formula x=2a−b±b2−4ac
x=22±(−2)2−4(−27)
Simplify the expression
More Steps
Evaluate
(−2)2−4(−27)
Multiply the numbers
More Steps
Evaluate
4(−27)
Multiplying or dividing an odd number of negative terms equals a negative
−4×27
Multiply the numbers
−108
(−2)2−(−108)
Rewrite the expression
22−(−108)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+108
Evaluate the power
4+108
Add the numbers
112
x=22±112
Simplify the radical expression
More Steps
Evaluate
112
Write the expression as a product where the root of one of the factors can be evaluated
16×7
Write the number in exponential form with the base of 4
42×7
The root of a product is equal to the product of the roots of each factor
42×7
Reduce the index of the radical and exponent with 2
47
x=22±47
Separate the equation into 2 possible cases
x=22+47x=22−47
Simplify the expression
More Steps
Evaluate
x=22+47
Divide the terms
More Steps
Evaluate
22+47
Rewrite the expression
22(1+27)
Reduce the fraction
1+27
x=1+27
x=1+27x=22−47
Simplify the expression
More Steps
Evaluate
x=22−47
Divide the terms
More Steps
Evaluate
22−47
Rewrite the expression
22(1−27)
Reduce the fraction
1−27
x=1−27
x=1+27x=1−27
Solution
x1=1−27,x2=1+27
Alternative Form
x1≈−4.291503,x2≈6.291503
Show Solution
