Question
Solve the equation
x1=−25,x2=20
Evaluate
x200−x+5200=2
Find the domain
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Evaluate
{x=0x+5=0
Calculate
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Evaluate
x+5=0
Move the constant to the right side
x=0−5
Removing 0 doesn't change the value,so remove it from the expression
x=−5
{x=0x=−5
Find the intersection
x∈(−∞,−5)∪(−5,0)∪(0,+∞)
x200−x+5200=2,x∈(−∞,−5)∪(−5,0)∪(0,+∞)
Multiply both sides of the equation by LCD
(x200−x+5200)x(x+5)=2x(x+5)
Simplify the equation
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Evaluate
(x200−x+5200)x(x+5)
Apply the distributive property
x200×x(x+5)−x+5200×x(x+5)
Simplify
200(x+5)−200x
Expand the expression
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Calculate
200(x+5)
Apply the distributive property
200x+200×5
Multiply the numbers
200x+1000
200x+1000−200x
The sum of two opposites equals 0
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Evaluate
200x−200x
Collect like terms
(200−200)x
Add the coefficients
0×x
Calculate
0
0+1000
Remove 0
1000
1000=2x(x+5)
Simplify the equation
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Evaluate
2x(x+5)
Apply the distributive property
2x×x+2x×5
Multiply the terms
2x2+2x×5
Multiply the numbers
2x2+10x
1000=2x2+10x
Swap the sides of the equation
2x2+10x=1000
Move the expression to the left side
2x2+10x−1000=0
Factor the expression
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Evaluate
2x2+10x−1000
Rewrite the expression
2x2+2×5x−2×500
Factor out 2 from the expression
2(x2+5x−500)
Factor the expression
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Evaluate
x2+5x−500
Rewrite the expression
x2+(25−20)x−500
Calculate
x2+25x−20x−500
Rewrite the expression
x×x+x×25−20x−20×25
Factor out x from the expression
x(x+25)−20x−20×25
Factor out −20 from the expression
x(x+25)−20(x+25)
Factor out x+25 from the expression
(x−20)(x+25)
2(x−20)(x+25)
2(x−20)(x+25)=0
Divide the terms
(x−20)(x+25)=0
When the product of factors equals 0,at least one factor is 0
x−20=0x+25=0
Solve the equation for x
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Evaluate
x−20=0
Move the constant to the right-hand side and change its sign
x=0+20
Removing 0 doesn't change the value,so remove it from the expression
x=20
x=20x+25=0
Solve the equation for x
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Evaluate
x+25=0
Move the constant to the right-hand side and change its sign
x=0−25
Removing 0 doesn't change the value,so remove it from the expression
x=−25
x=20x=−25
Check if the solution is in the defined range
x=20x=−25,x∈(−∞,−5)∪(−5,0)∪(0,+∞)
Find the intersection of the solution and the defined range
x=20x=−25
Solution
x1=−25,x2=20
Show Solution
