Algebra
Calculus
Trigonometry
Matrix
Question
Find the excluded values
b=6
Evaluate
b−68b2−41b−27
To find the excluded values,set the denominators equal to 0
b−6=0
Move the constant to the right-hand side and change its sign
b=0+6
Solution
b=6
Show Solution
Divide the polynomials
8b+7+b−615
Evaluate
b−68b2−41b−27
Solution
8b+7+b−615
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Find the roots
b1=1641−2545,b2=1641+2545
Alternative Form
b1≈−0.5905,b2≈5.7155
Evaluate
b−68b2−41b−27
To find the roots of the expression,set the expression equal to 0
b−68b2−41b−27=0
Find the domain
More Steps
Evaluate
b−6=0
Move the constant to the right side
b=0+6
Removing 0 doesn't change the value,so remove it from the expression
b=6
b−68b2−41b−27=0,b=6
Calculate
b−68b2−41b−27=0
Cross multiply
8b2−41b−27=(b−6)×0
Simplify the equation
8b2−41b−27=0
Substitute a=8,b=−41 and c=−27 into the quadratic formula b=2a−b±b2−4ac
b=2×841±(−41)2−4×8(−27)
Simplify the expression
b=1641±(−41)2−4×8(−27)
Simplify the expression
More Steps
Evaluate
(−41)2−4×8(−27)
Multiply
More Steps
Multiply the terms
4×8(−27)
Rewrite the expression
−4×8×27
Multiply the terms
−864
(−41)2−(−864)
Rewrite the expression
412−(−864)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
412+864
Evaluate the power
1681+864
Add the numbers
2545
b=1641±2545
Separate the equation into 2 possible cases
b=1641+2545b=1641−2545
Check if the solution is in the defined range
b=1641+2545b=1641−2545,b=6
Find the intersection of the solution and the defined range
b=1641+2545b=1641−2545
Solution
b1=1641−2545,b2=1641+2545
Alternative Form
b1≈−0.5905,b2≈5.7155
Show Solution