Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
y1=6−314,y2=6+314
Alternative Form
y1≈−5.224972,y2≈17.224972
Evaluate
y2−12y−90
To find the roots of the expression,set the expression equal to 0
y2−12y−90=0
Substitute a=1,b=−12 and c=−90 into the quadratic formula y=2a−b±b2−4ac
y=212±(−12)2−4(−90)
Simplify the expression
More Steps
Evaluate
(−12)2−4(−90)
Multiply the numbers
More Steps
Evaluate
4(−90)
Multiplying or dividing an odd number of negative terms equals a negative
−4×90
Multiply the numbers
−360
(−12)2−(−360)
Rewrite the expression
122−(−360)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+360
Evaluate the power
144+360
Add the numbers
504
y=212±504
Simplify the radical expression
More Steps
Evaluate
504
Write the expression as a product where the root of one of the factors can be evaluated
36×14
Write the number in exponential form with the base of 6
62×14
The root of a product is equal to the product of the roots of each factor
62×14
Reduce the index of the radical and exponent with 2
614
y=212±614
Separate the equation into 2 possible cases
y=212+614y=212−614
Simplify the expression
More Steps
Evaluate
y=212+614
Divide the terms
More Steps
Evaluate
212+614
Rewrite the expression
22(6+314)
Reduce the fraction
6+314
y=6+314
y=6+314y=212−614
Simplify the expression
More Steps
Evaluate
y=212−614
Divide the terms
More Steps
Evaluate
212−614
Rewrite the expression
22(6−314)
Reduce the fraction
6−314
y=6−314
y=6+314y=6−314
Solution
y1=6−314,y2=6+314
Alternative Form
y1≈−5.224972,y2≈17.224972
Show Solution
