Question
Find the roots
Find the roots of the algebra expression
x1=55−35,x2=55+35
Alternative Form
x1≈−0.183216,x2≈2.183216
Evaluate
−5x2+10x+2
To find the roots of the expression,set the expression equal to 0
−5x2+10x+2=0
Multiply both sides
5x2−10x−2=0
Substitute a=5,b=−10 and c=−2 into the quadratic formula x=2a−b±b2−4ac
x=2×510±(−10)2−4×5(−2)
Simplify the expression
x=1010±(−10)2−4×5(−2)
Simplify the expression
More Steps
Evaluate
(−10)2−4×5(−2)
Multiply
More Steps
Multiply the terms
4×5(−2)
Rewrite the expression
−4×5×2
Multiply the terms
−40
(−10)2−(−40)
Rewrite the expression
102−(−40)
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+40
Evaluate the power
100+40
Add the numbers
140
x=1010±140
Simplify the radical expression
More Steps
Evaluate
140
Write the expression as a product where the root of one of the factors can be evaluated
4×35
Write the number in exponential form with the base of 2
22×35
The root of a product is equal to the product of the roots of each factor
22×35
Reduce the index of the radical and exponent with 2
235
x=1010±235
Separate the equation into 2 possible cases
x=1010+235x=1010−235
Simplify the expression
More Steps
Evaluate
x=1010+235
Divide the terms
More Steps
Evaluate
1010+235
Rewrite the expression
102(5+35)
Cancel out the common factor 2
55+35
x=55+35
x=55+35x=1010−235
Simplify the expression
More Steps
Evaluate
x=1010−235
Divide the terms
More Steps
Evaluate
1010−235
Rewrite the expression
102(5−35)
Cancel out the common factor 2
55−35
x=55−35
x=55+35x=55−35
Solution
x1=55−35,x2=55+35
Alternative Form
x1≈−0.183216,x2≈2.183216
Show Solution