Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=3,x2=5
Evaluate
6x2−50=4x−10
Find the domain
More Steps
Evaluate
6x2−50≥0
Move the constant to the right side
6x2≥50
Divide both sides
66x2≥650
Divide the numbers
x2≥650
Cancel out the common factor 2
x2≥325
Take the 2-th root on both sides of the inequality
x2≥325
Calculate
∣x∣≥353
Separate the inequality into 2 possible cases
x≥353x≤−353
Find the union
x∈(−∞,−353]∪[353,+∞)
6x2−50=4x−10,x∈(−∞,−353]∪[353,+∞)
Evaluate
6x2−50=4x−10,4x−10≥0
Evaluate
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Evaluate
4x−10≥0
Move the constant to the right side
4x≥0+10
Removing 0 doesn't change the value,so remove it from the expression
4x≥10
Divide both sides
44x≥410
Divide the numbers
x≥410
Cancel out the common factor 2
x≥25
6x2−50=4x−10,x≥25
Solve the equation for x
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Evaluate
6x2−50=4x−10
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(6x2−50)2=(4x−10)2
Evaluate the power
6x2−50=16x2−80x+100
Move the expression to the left side
6x2−50−(16x2−80x+100)=0
Subtract the terms
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Evaluate
6x2−50−(16x2−80x+100)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
6x2−50−16x2+80x−100
Subtract the terms
−10x2−50+80x−100
Subtract the numbers
−10x2−150+80x
−10x2−150+80x=0
Factor the expression
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Evaluate
−10x2−150+80x
Evaluate
−10x2+80x−150
Rewrite the expression
−10x2+10×8x−10×15
Factor out −10 from the expression
−10(x2−8x+15)
Factor the expression
−10(x−5)(x−3)
−10(x−5)(x−3)=0
Divide the terms
(x−5)(x−3)=0
When the product of factors equals 0,at least one factor is 0
x−5=0x−3=0
Solve the equation for x
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Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=5x−3=0
Solve the equation for x
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=5x=3
x=5x=3,x≥25
Find the intersection
x=5x=3
Check if the solution is in the defined range
x=5x=3,x∈(−∞,−353]∪[353,+∞)
Find the intersection of the solution and the defined range
x=5x=3
Check the solution
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Check the solution
6×52−50=4×5−10
Simplify
10=10
Evaluate
true
x=5x=3
Check the solution
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Check the solution
6×32−50=4×3−10
Simplify
2=2
Evaluate
true
x=5x=3
Solution
x1=3,x2=5
Show Solution
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