Question
Find the roots
Find the roots of the algebra expression
x1=21−614,x2=21+614
Alternative Form
x1≈−1.449944,x2≈43.449944
Evaluate
x2−42x−63
To find the roots of the expression,set the expression equal to 0
x2−42x−63=0
Substitute a=1,b=−42 and c=−63 into the quadratic formula x=2a−b±b2−4ac
x=242±(−42)2−4(−63)
Simplify the expression
More Steps
Evaluate
(−42)2−4(−63)
Multiply the numbers
More Steps
Evaluate
4(−63)
Multiplying or dividing an odd number of negative terms equals a negative
−4×63
Multiply the numbers
−252
(−42)2−(−252)
Rewrite the expression
422−(−252)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
422+252
Evaluate the power
1764+252
Add the numbers
2016
x=242±2016
Simplify the radical expression
More Steps
Evaluate
2016
Write the expression as a product where the root of one of the factors can be evaluated
144×14
Write the number in exponential form with the base of 12
122×14
The root of a product is equal to the product of the roots of each factor
122×14
Reduce the index of the radical and exponent with 2
1214
x=242±1214
Separate the equation into 2 possible cases
x=242+1214x=242−1214
Simplify the expression
More Steps
Evaluate
x=242+1214
Divide the terms
More Steps
Evaluate
242+1214
Rewrite the expression
22(21+614)
Reduce the fraction
21+614
x=21+614
x=21+614x=242−1214
Simplify the expression
More Steps
Evaluate
x=242−1214
Divide the terms
More Steps
Evaluate
242−1214
Rewrite the expression
22(21−614)
Reduce the fraction
21−614
x=21−614
x=21+614x=21−614
Solution
x1=21−614,x2=21+614
Alternative Form
x1≈−1.449944,x2≈43.449944
Show Solution