Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
xx3−8x2−12x−3
Evaluate
x×1x3−8x2−12x−3
Solution
xx3−8x2−12x−3
Show Solution
Find the excluded values
x=0
Evaluate
x×1x3−8x2−12x−3
To find the excluded values,set the denominators equal to 0
x×1=0
Solution
x=0
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Find the roots
x1=−1,x2=29−93,x3=29+93
Alternative Form
x1=−1,x2≈−0.321825,x3≈9.321825
Evaluate
x×1x3−8x2−12x−3
To find the roots of the expression,set the expression equal to 0
x×1x3−8x2−12x−3=0
Any expression multiplied by 1 remains the same
x×1x3−8x2−12x−3=0,x=0
Calculate
x×1x3−8x2−12x−3=0
Any expression multiplied by 1 remains the same
xx3−8x2−12x−3=0
Cross multiply
x3−8x2−12x−3=x×0
Simplify the equation
x3−8x2−12x−3=0
Factor the expression
(x+1)(x2−9x−3)=0
Separate the equation into 2 possible cases
x+1=0x2−9x−3=0
Solve the equation
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=−1x2−9x−3=0
Solve the equation
More Steps
Evaluate
x2−9x−3=0
Substitute a=1,b=−9 and c=−3 into the quadratic formula x=2a−b±b2−4ac
x=29±(−9)2−4(−3)
Simplify the expression
More Steps
Evaluate
(−9)2−4(−3)
Multiply the numbers
(−9)2−(−12)
Rewrite the expression
92−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
92+12
Evaluate the power
81+12
Add the numbers
93
x=29±93
Separate the equation into 2 possible cases
x=29+93x=29−93
x=−1x=29+93x=29−93
Check if the solution is in the defined range
x=−1x=29+93x=29−93,x=0
Find the intersection of the solution and the defined range
x=−1x=29+93x=29−93
Solution
x1=−1,x2=29−93,x3=29+93
Alternative Form
x1=−1,x2≈−0.321825,x3≈9.321825
Show Solution