Question
Solve the equation
x=14
Evaluate
44−2x=x−10
Find the domain
More Steps

Evaluate
44−2x≥0
Move the constant to the right side
−2x≥0−44
Removing 0 doesn't change the value,so remove it from the expression
−2x≥−44
Change the signs on both sides of the inequality and flip the inequality sign
2x≤44
Divide both sides
22x≤244
Divide the numbers
x≤244
Divide the numbers
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Evaluate
244
Reduce the numbers
122
Calculate
22
x≤22
44−2x=x−10,x≤22
Evaluate
44−2x=x−10,x−10≥0
Evaluate
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Evaluate
x−10≥0
Move the constant to the right side
x≥0+10
Removing 0 doesn't change the value,so remove it from the expression
x≥10
44−2x=x−10,x≥10
Solve the equation for x
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Evaluate
44−2x=x−10
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(44−2x)2=(x−10)2
Evaluate the power
44−2x=x2−20x+100
Move the expression to the left side
44−2x−(x2−20x+100)=0
Subtract the terms
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Evaluate
44−2x−(x2−20x+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
44−2x−x2+20x−100
Subtract the numbers
−56−2x−x2+20x
Add the terms
−56+18x−x2
−56+18x−x2=0
Factor the expression
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Evaluate
−56+18x−x2
Rewrite the expression
−56+(14+4)x−x2
Calculate
−56+14x+4x−x2
Rewrite the expression
−14×4+14x+x×4−x×x
Factor out −14 from the expression
−14(4−x)+x×4−x×x
Factor out x from the expression
−14(4−x)+x(4−x)
Factor out 4−x from the expression
(−14+x)(4−x)
(−14+x)(4−x)=0
When the product of factors equals 0,at least one factor is 0
−14+x=04−x=0
Solve the equation for x
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Evaluate
−14+x=0
Move the constant to the right-hand side and change its sign
x=0+14
Removing 0 doesn't change the value,so remove it from the expression
x=14
x=144−x=0
Solve the equation for x
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Evaluate
4−x=0
Move the constant to the right-hand side and change its sign
−x=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x=−4
Change the signs on both sides of the equation
x=4
x=14x=4
x=14x=4,x≥10
Find the intersection
x=14
Check if the solution is in the defined range
x=14,x≤22
Find the intersection of the solution and the defined range
x=14
Solution
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Check the solution
44−2×14=14−10
Simplify
4=4
Evaluate
true
x=14
Show Solution
