Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=4
Evaluate
x−3=x−5
Find the domain
x−3=x−5,x≥0
Move the constant to the right side
x=x−5−(−3)
Calculate
x=x−2
Evaluate
x=x−2,x−2≥0
Evaluate
More Steps
Evaluate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
x=x−2,x≥2
Solve the equation for x
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Evaluate
x=x−2
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(x)2=(x−2)2
Evaluate the power
x=x2−4x+4
Move the expression to the left side
x−(x2−4x+4)=0
Subtract the terms
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Evaluate
x−(x2−4x+4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x−x2+4x−4
Add the terms
5x−x2−4
5x−x2−4=0
Factor the expression
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Evaluate
5x−x2−4
Reorder the terms
−x2+5x−4
Rewrite the expression
−x2+(1+4)x−4
Calculate
−x2+x+4x−4
Rewrite the expression
−x×x+x+4x−4
Factor out −x from the expression
−x(x−1)+4x−4
Factor out 4 from the expression
−x(x−1)+4(x−1)
Factor out x−1 from the expression
(−x+4)(x−1)
(−x+4)(x−1)=0
When the product of factors equals 0,at least one factor is 0
−x+4=0x−1=0
Solve the equation for x
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Evaluate
−x+4=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=4x−1=0
Solve the equation for x
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Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=4x=1
x=4x=1,x≥2
Find the intersection
x=4
Check if the solution is in the defined range
x=4,x≥0
Find the intersection of the solution and the defined range
x=4
Solution
More Steps
Check the solution
4−3=4−5
Simplify
−1=−1
Evaluate
true
x=4
Show Solution
Graph
