Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
a1=−2,a2=1
Evaluate
∣a2∣−∣a−2∣=0
Simplify
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Evaluate
∣a2∣−∣a−2∣
When the expression in absolute value bars is not negative, remove the bars
a2−∣a−2∣
Calculate
∣a∣−∣a−2∣
∣a∣−∣a−2∣=0
Separate the equation into 4 possible cases
a−a−2=0,a≥0,a−2≥0a−−(a−2)=0,a≥0,a−2<0−a−a−2=0,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the equation
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Evaluate
a−a−2=0
Move the variable to the right-hand side and change its sign
−a−2=−a
Divide both sides of the equation by −1
a−2=a
Evaluate
a−2=a,a≥0
Solve the equation for a
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Evaluate
a−2=a
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(a−2)2=a2
Evaluate the power
a−2=a2
Move the expression to the left side
a−2−a2=0
Rewrite in standard form
−a2+a−2=0
Multiply both sides
a2−a+2=0
Substitute a=1,b=−1 and c=2 into the quadratic formula a=2a−b±b2−4ac
a=21±(−1)2−4×2
Simplify the expression
a=21±−7
The expression is undefined in the set of real numbers
a∈/R
a∈/R,a≥0
Find the intersection
a∈/R
a∈/R,a≥0,a−2≥0a−−(a−2)=0,a≥0,a−2<0−a−a−2=0,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the inequality
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Evaluate
a−2≥0
Move the constant to the right side
a≥0+2
Removing 0 doesn't change the value,so remove it from the expression
a≥2
a∈/R,a≥0,a≥2a−−(a−2)=0,a≥0,a−2<0−a−a−2=0,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the equation
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Evaluate
a−−(a−2)=0
Calculate
a−−a+2=0
Move the variable to the right-hand side and change its sign
−−a+2=−a
Divide both sides of the equation by −1
−a+2=a
Evaluate
−a+2=a,a≥0
Solve the equation for a
More Steps
Evaluate
−a+2=a
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(−a+2)2=a2
Evaluate the power
−a+2=a2
Move the expression to the left side
−a+2−a2=0
Factor the expression
(1−a)(2+a)=0
When the product of factors equals 0,at least one factor is 0
1−a=02+a=0
Solve the equation for a
a=12+a=0
Solve the equation for a
a=1a=−2
a=1a=−2,a≥0
Find the intersection
a=1
a∈/R,a≥0,a≥2a=1,a≥0,a−2<0−a−a−2=0,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the inequality
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Evaluate
a−2<0
Move the constant to the right side
a<0+2
Removing 0 doesn't change the value,so remove it from the expression
a<2
a∈/R,a≥0,a≥2a=1,a≥0,a<2−a−a−2=0,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the equation
More Steps
Evaluate
−a−a−2=0
Move the variable to the right-hand side and change its sign
−a−2=a
Change the signs
a−2=−a
Evaluate
a−2=−a,−a≥0
Change the signs on both sides of the inequality and flip the inequality sign
a−2=−a,a≤0
Solve the equation for a
More Steps
Evaluate
a−2=−a
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(a−2)2=(−a)2
Evaluate the power
a−2=a2
Move the expression to the left side
a−2−a2=0
Rewrite in standard form
−a2+a−2=0
Multiply both sides
a2−a+2=0
Substitute a=1,b=−1 and c=2 into the quadratic formula a=2a−b±b2−4ac
a=21±(−1)2−4×2
Simplify the expression
a=21±−7
The expression is undefined in the set of real numbers
a∈/R
a∈/R,a≤0
Find the intersection
a∈/R
a∈/R,a≥0,a≥2a=1,a≥0,a<2a∈/R,a<0,a−2≥0−a−−(a−2)=0,a<0,a−2<0
Solve the inequality
More Steps
Evaluate
a−2≥0
Move the constant to the right side
a≥0+2
Removing 0 doesn't change the value,so remove it from the expression
a≥2
a∈/R,a≥0,a≥2a=1,a≥0,a<2a∈/R,a<0,a≥2−a−−(a−2)=0,a<0,a−2<0
Solve the equation
More Steps
Evaluate
−a−−(a−2)=0
Calculate
−a−−a+2=0
Move the variable to the right-hand side and change its sign
−−a+2=a
Change the signs
−a+2=−a
Evaluate
−a+2=−a,−a≥0
Change the signs on both sides of the inequality and flip the inequality sign
−a+2=−a,a≤0
Solve the equation for a
More Steps
Evaluate
−a+2=−a
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(−a+2)2=(−a)2
Evaluate the power
−a+2=a2
Move the expression to the left side
−a+2−a2=0
Factor the expression
(1−a)(2+a)=0
When the product of factors equals 0,at least one factor is 0
1−a=02+a=0
Solve the equation for a
a=12+a=0
Solve the equation for a
a=1a=−2
a=1a=−2,a≤0
Find the intersection
a=−2
a∈/R,a≥0,a≥2a=1,a≥0,a<2a∈/R,a<0,a≥2a=−2,a<0,a−2<0
Solve the inequality
More Steps
Evaluate
a−2<0
Move the constant to the right side
a<0+2
Removing 0 doesn't change the value,so remove it from the expression
a<2
a∈/R,a≥0,a≥2a=1,a≥0,a<2a∈/R,a<0,a≥2a=−2,a<0,a<2
Find the intersection
a∈/Ra=1,a≥0,a<2a∈/R,a<0,a≥2a=−2,a<0,a<2
Find the intersection
a∈/Ra=1a∈/R,a<0,a≥2a=−2,a<0,a<2
Find the intersection
a∈/Ra=1a∈/Ra=−2,a<0,a<2
Find the intersection
a∈/Ra=1a∈/Ra=−2
Find the union
a=1a=−2
Check the solution
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Check the solution
∣12∣−∣1−2∣=0
Simplify
0=0
Evaluate
true
a=1a=−2
Check the solution
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Check the solution
(−2)2−∣−2−2∣=0
Simplify
0=0
Evaluate
true
a=1a=−2
Solution
a1=−2,a2=1
Show Solution
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