Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=0,x2=106,x3=134
Evaluate
x2−8x×15−2x×7=0
Simplify
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Evaluate
x2−8x×15−2x×7
Multiply the terms
x2−120x−2x×7
Multiply the terms
x2−120x−14x
x2−120x−14x=0
Separate the equation into 2 possible cases
x2−120x−14x=0,x2−120x≥0−(x2−120x)−14x=0,x2−120x<0
Solve the equation
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Evaluate
x2−120x−14x=0
Calculate
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Evaluate
−120x−14x
Collect like terms by calculating the sum or difference of their coefficients
(−120−14)x
Subtract the numbers
−134x
x2−134x=0
Factor the expression
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Evaluate
x2−134x
Rewrite the expression
x×x−x×134
Factor out x from the expression
x(x−134)
x(x−134)=0
When the product of factors equals 0,at least one factor is 0
x=0x−134=0
Solve the equation for x
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Evaluate
x−134=0
Move the constant to the right-hand side and change its sign
x=0+134
Removing 0 doesn't change the value,so remove it from the expression
x=134
x=0x=134
x=0x=134,x2−120x≥0−(x2−120x)−14x=0,x2−120x<0
Solve the inequality
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Evaluate
x2−120x≥0
Add the same value to both sides
x2−120x+3600≥3600
Evaluate
(x−60)2≥3600
Take the 2-th root on both sides of the inequality
(x−60)2≥3600
Calculate
∣x−60∣≥60
Separate the inequality into 2 possible cases
x−60≥60x−60≤−60
Calculate
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Evaluate
x−60≥60
Move the constant to the right side
x≥60+60
Add the numbers
x≥120
x≥120x−60≤−60
Cancel equal terms on both sides of the expression
x≥120x≤0
Find the union
x∈(−∞,0]∪[120,+∞)
x=0x=134,x∈(−∞,0]∪[120,+∞)−(x2−120x)−14x=0,x2−120x<0
Solve the equation
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Evaluate
−(x2−120x)−14x=0
Calculate
−x2+120x−14x=0
Calculate
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Evaluate
120x−14x
Collect like terms by calculating the sum or difference of their coefficients
(120−14)x
Subtract the numbers
106x
−x2+106x=0
Factor the expression
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Evaluate
−x2+106x
Rewrite the expression
−x×x+x×106
Factor out −x from the expression
−x(x−106)
−x(x−106)=0
When the product of factors equals 0,at least one factor is 0
−x=0x−106=0
Solve the equation for x
x=0x−106=0
Solve the equation for x
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Evaluate
x−106=0
Move the constant to the right-hand side and change its sign
x=0+106
Removing 0 doesn't change the value,so remove it from the expression
x=106
x=0x=106
x=0x=134,x∈(−∞,0]∪[120,+∞)x=0x=106,x2−120x<0
Solve the inequality
More Steps
Evaluate
x2−120x<0
Add the same value to both sides
x2−120x+3600<3600
Evaluate
(x−60)2<3600
Take the 2-th root on both sides of the inequality
(x−60)2<3600
Calculate
∣x−60∣<60
Separate the inequality into 2 possible cases
{x−60<60x−60>−60
Calculate
More Steps
Evaluate
x−60<60
Move the constant to the right side
x<60+60
Add the numbers
x<120
{x<120x−60>−60
Cancel equal terms on both sides of the expression
{x<120x>0
Find the intersection
0<x<120
x=0x=134,x∈(−∞,0]∪[120,+∞)x=0x=106,0<x<120
Find the intersection
x=0x=134x=0x=106,0<x<120
Find the intersection
x=0x=134x=106
Solution
x1=0,x2=106,x3=134
Show Solution
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