Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=5−52,x2=5+52
Alternative Form
x1≈−2.071068,x2≈12.071068
Evaluate
x2−10x−25
To find the roots of the expression,set the expression equal to 0
x2−10x−25=0
Substitute a=1,b=−10 and c=−25 into the quadratic formula x=2a−b±b2−4ac
x=210±(−10)2−4(−25)
Simplify the expression
More Steps
Evaluate
(−10)2−4(−25)
Multiply the numbers
More Steps
Evaluate
4(−25)
Multiplying or dividing an odd number of negative terms equals a negative
−4×25
Multiply the numbers
−100
(−10)2−(−100)
Rewrite the expression
102−(−100)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
102+100
Evaluate the power
100+100
Add the numbers
200
x=210±200
Simplify the radical expression
More Steps
Evaluate
200
Write the expression as a product where the root of one of the factors can be evaluated
100×2
Write the number in exponential form with the base of 10
102×2
The root of a product is equal to the product of the roots of each factor
102×2
Reduce the index of the radical and exponent with 2
102
x=210±102
Separate the equation into 2 possible cases
x=210+102x=210−102
Simplify the expression
More Steps
Evaluate
x=210+102
Divide the terms
More Steps
Evaluate
210+102
Rewrite the expression
22(5+52)
Reduce the fraction
5+52
x=5+52
x=5+52x=210−102
Simplify the expression
More Steps
Evaluate
x=210−102
Divide the terms
More Steps
Evaluate
210−102
Rewrite the expression
22(5−52)
Reduce the fraction
5−52
x=5−52
x=5+52x=5−52
Solution
x1=5−52,x2=5+52
Alternative Form
x1≈−2.071068,x2≈12.071068
Show Solution
