Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=1−2,x2=2,x3=1+2
Alternative Form
x1≈−0.414214,x2=2,x3≈2.414214
Evaluate
x×1x−2=(x−2)2
Find the domain
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Evaluate
x×1=0
Any expression multiplied by 1 remains the same
x=0
x×1x−2=(x−2)2,x=0
Any expression multiplied by 1 remains the same
xx−2=(x−2)2
Cross multiply
x−2=x(x−2)2
Expand the expression
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Evaluate
x(x−2)2
Expand the expression
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Evaluate
(x−2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×2+22
Calculate
x2−4x+4
x(x2−4x+4)
Apply the distributive property
x×x2−x×4x+x×4
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
x3−x×4x+x×4
Multiply the terms
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Evaluate
x×4x
Use the commutative property to reorder the terms
4x×x
Multiply the terms
4x2
x3−4x2+x×4
Use the commutative property to reorder the terms
x3−4x2+4x
x−2=x3−4x2+4x
Move the expression to the left side
x−2−(x3−4x2+4x)=0
Subtract the terms
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Evaluate
x−2−(x3−4x2+4x)
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−2−x3+4x2−4x
Subtract the terms
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Evaluate
x−4x
Collect like terms by calculating the sum or difference of their coefficients
(1−4)x
Subtract the numbers
−3x
−3x−2−x3+4x2
−3x−2−x3+4x2=0
Factor the expression
(−2+x)(1−x2+2x)=0
Separate the equation into 2 possible cases
−2+x=01−x2+2x=0
Solve the equation
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Evaluate
−2+x=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=21−x2+2x=0
Solve the equation
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Evaluate
1−x2+2x=0
Rewrite in standard form
−x2+2x+1=0
Multiply both sides
x2−2x−1=0
Substitute a=1,b=−2 and c=−1 into the quadratic formula x=2a−b±b2−4ac
x=22±(−2)2−4(−1)
Simplify the expression
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Evaluate
(−2)2−4(−1)
Simplify
(−2)2−(−4)
Rewrite the expression
22−(−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
22+4
Evaluate the power
4+4
Add the numbers
8
x=22±8
Simplify the radical expression
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Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
x=22±22
Separate the equation into 2 possible cases
x=22+22x=22−22
Simplify the expression
x=1+2x=22−22
Simplify the expression
x=1+2x=1−2
x=2x=1+2x=1−2
Check if the solution is in the defined range
x=2x=1+2x=1−2,x=0
Find the intersection of the solution and the defined range
x=2x=1+2x=1−2
Solution
x1=1−2,x2=2,x3=1+2
Alternative Form
x1≈−0.414214,x2=2,x3≈2.414214
Show Solution
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