Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
−(1000−x)(200−x)
Evaluate
1200x−200000−x2
Reorder the terms
−200000+1200x−x2
Rewrite the expression
−200000+(1000+200)x−x2
Calculate
−200000+1000x+200x−x2
Rewrite the expression
−1000×200+1000x+x×200−x×x
Factor out −1000 from the expression
−1000(200−x)+x×200−x×x
Factor out x from the expression
−1000(200−x)+x(200−x)
Factor out 200−x from the expression
(−1000+x)(200−x)
Solution
−(1000−x)(200−x)
Show Solution
Find the roots
x1=200,x2=1000
Evaluate
1200x−200000−x2
To find the roots of the expression,set the expression equal to 0
1200x−200000−x2=0
Factor the expression
More Steps
Evaluate
1200x−200000−x2
Reorder the terms
−200000+1200x−x2
Rewrite the expression
−200000+(1000+200)x−x2
Calculate
−200000+1000x+200x−x2
Rewrite the expression
−1000×200+1000x+x×200−x×x
Factor out −1000 from the expression
−1000(200−x)+x×200−x×x
Factor out x from the expression
−1000(200−x)+x(200−x)
Factor out 200−x from the expression
(−1000+x)(200−x)
(−1000+x)(200−x)=0
When the product of factors equals 0,at least one factor is 0
−1000+x=0200−x=0
Solve the equation for x
More Steps
Evaluate
−1000+x=0
Move the constant to the right-hand side and change its sign
x=0+1000
Removing 0 doesn't change the value,so remove it from the expression
x=1000
x=1000200−x=0
Solve the equation for x
More Steps
Evaluate
200−x=0
Move the constant to the right-hand side and change its sign
−x=0−200
Removing 0 doesn't change the value,so remove it from the expression
−x=−200
Change the signs on both sides of the equation
x=200
x=1000x=200
Solution
x1=200,x2=1000
Show Solution