Algebra
Calculus
Trigonometry
Matrix
Question
x2−6x−∣x−6∣
Find the roots
x1=−1,x2=6
Evaluate
x2−6x−∣x−6∣
To find the roots of the expression,set the expression equal to 0
x2−6x−∣x−6∣=0
Rewrite the expression
x2−6x−∣x−6∣=0
Separate the equation into 2 possible cases
x2−6x−(x−6)=0,x−6≥0x2−6x−(−(x−6))=0,x−6<0
Solve the equation
More Steps
Evaluate
x2−6x−(x−6)=0
Calculate
x2−6x−x+6=0
Calculate
More Steps
Evaluate
−6x−x
Collect like terms by calculating the sum or difference of their coefficients
(−6−1)x
Subtract the numbers
−7x
x2−7x+6=0
Factor the expression
More Steps
Evaluate
x2−7x+6
Rewrite the expression
x2+(−1−6)x+6
Calculate
x2−x−6x+6
Rewrite the expression
x×x−x−6x+6
Factor out x from the expression
x(x−1)−6x+6
Factor out −6 from the expression
x(x−1)−6(x−1)
Factor out x−1 from the expression
(x−6)(x−1)
(x−6)(x−1)=0
When the product of factors equals 0,at least one factor is 0
x−6=0x−1=0
Solve the equation for x
More Steps
Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=6x−1=0
Solve the equation for x
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=6x=1
x=6x=1,x−6≥0x2−6x−(−(x−6))=0,x−6<0
Solve the inequality
More Steps
Evaluate
x−6≥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
x=6x=1,x≥6x2−6x−(−(x−6))=0,x−6<0
Solve the equation
More Steps
Evaluate
x2−6x−(−(x−6))=0
Calculate
x2−6x+x−6=0
Calculate
More Steps
Evaluate
−6x+x
Collect like terms by calculating the sum or difference of their coefficients
(−6+1)x
Add the numbers
−5x
x2−5x−6=0
Factor the expression
More Steps
Evaluate
x2−5x−6
Rewrite the expression
x2+(1−6)x−6
Calculate
x2+x−6x−6
Rewrite the expression
x×x+x−6x−6
Factor out x from the expression
x(x+1)−6x−6
Factor out −6 from the expression
x(x+1)−6(x+1)
Factor out x+1 from the expression
(x−6)(x+1)
(x−6)(x+1)=0
When the product of factors equals 0,at least one factor is 0
x−6=0x+1=0
Solve the equation for x
More Steps
Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=6x+1=0
Solve the equation for x
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=6x=−1
x=6x=1,x≥6x=6x=−1,x−6<0
Solve the inequality
More Steps
Evaluate
x−6<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
x=6x=1,x≥6x=6x=−1,x<6
Find the intersection
x=6x=6x=−1,x<6
Find the intersection
x=6x=−1
Solution
x1=−1,x2=6
Show Solution
