Algebra
Calculus
Trigonometry
Matrix
Question
x2−2x6−x
Factor the expression
(x−26−x)x
Evaluate
x2−2x6−x
Rewrite the expression
x×x−26−x×x
Solution
(x−26−x)x
Show Solution
Find the roots
x1=−2−27,x2=0,x3=−2+27
Alternative Form
x1≈−7.291503,x2=0,x3≈3.291503
Evaluate
x2−2x6−x
To find the roots of the expression,set the expression equal to 0
x2−2x6−x=0
Find the domain
More Steps
Evaluate
6−x≥0
Move the constant to the right side
−x≥0−6
Removing 0 doesn't change the value,so remove it from the expression
−x≥−6
Change the signs on both sides of the inequality and flip the inequality sign
x≤6
x2−2x6−x=0,x≤6
Calculate
x2−2x6−x=0
Move the expression to the right-hand side and change its sign
−2x6−x=−x2
Divide both sides of the equation by −1
2x6−x=x2
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(2x6−x)2=(x2)2
Evaluate the power
24x2−4x3=x4
Move the expression to the left side
24x2−4x3−x4=0
Factor the expression
x2(24−4x−x2)=0
Separate the equation into 2 possible cases
x2=024−4x−x2=0
The only way a power can be 0 is when the base equals 0
x=024−4x−x2=0
Solve the equation
More Steps
Evaluate
24−4x−x2=0
Rewrite in standard form
−x2−4x+24=0
Multiply both sides
x2+4x−24=0
Substitute a=1,b=4 and c=−24 into the quadratic formula x=2a−b±b2−4ac
x=2−4±42−4(−24)
Simplify the expression
More Steps
Evaluate
42−4(−24)
Multiply the numbers
42−(−96)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+96
Evaluate the power
16+96
Add the numbers
112
x=2−4±112
Simplify the radical expression
More Steps
Evaluate
112
Write the expression as a product where the root of one of the factors can be evaluated
16×7
Write the number in exponential form with the base of 4
42×7
The root of a product is equal to the product of the roots of each factor
42×7
Reduce the index of the radical and exponent with 2
47
x=2−4±47
Separate the equation into 2 possible cases
x=2−4+47x=2−4−47
Simplify the expression
x=−2+27x=2−4−47
Simplify the expression
x=−2+27x=−2−27
x=0x=−2+27x=−2−27
Check if the solution is in the defined range
x=0x=−2+27x=−2−27,x≤6
Find the intersection of the solution and the defined range
x=0x=−2+27x=−2−27
Solution
x1=−2−27,x2=0,x3=−2+27
Alternative Form
x1≈−7.291503,x2=0,x3≈3.291503
Show Solution