Algebra Examples

Solve for x square root of (x-1)^2=1-x
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Divide by .
Step 2.3
Simplify the left side.
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Step 2.3.1
Multiply the exponents in .
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Step 2.3.1.1
Apply the power rule and multiply exponents, .
Step 2.3.1.2
Multiply by .
Step 2.4
Simplify the right side.
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Step 2.4.1
Simplify .
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Step 2.4.1.1
Rewrite as .
Step 2.4.1.2
Expand using the FOIL Method.
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Step 2.4.1.2.1
Apply the distributive property.
Step 2.4.1.2.2
Apply the distributive property.
Step 2.4.1.2.3
Apply the distributive property.
Step 2.4.1.3
Simplify and combine like terms.
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Step 2.4.1.3.1
Simplify each term.
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Step 2.4.1.3.1.1
Multiply by .
Step 2.4.1.3.1.2
Multiply by .
Step 2.4.1.3.1.3
Multiply by .
Step 2.4.1.3.1.4
Rewrite using the commutative property of multiplication.
Step 2.4.1.3.1.5
Multiply by by adding the exponents.
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Step 2.4.1.3.1.5.1
Move .
Step 2.4.1.3.1.5.2
Multiply by .
Step 2.4.1.3.1.6
Multiply by .
Step 2.4.1.3.1.7
Multiply by .
Step 2.4.1.3.2
Subtract from .
Step 3
Solve for .
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Step 3.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3.2
Simplify .
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Step 3.2.1
Rewrite.
Step 3.2.2
Rewrite as .
Step 3.2.3
Expand using the FOIL Method.
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Step 3.2.3.1
Apply the distributive property.
Step 3.2.3.2
Apply the distributive property.
Step 3.2.3.3
Apply the distributive property.
Step 3.2.4
Simplify and combine like terms.
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Step 3.2.4.1
Simplify each term.
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Step 3.2.4.1.1
Multiply by .
Step 3.2.4.1.2
Move to the left of .
Step 3.2.4.1.3
Rewrite as .
Step 3.2.4.1.4
Rewrite as .
Step 3.2.4.1.5
Multiply by .
Step 3.2.4.2
Subtract from .
Step 3.3
Move all terms containing to the left side of the equation.
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Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Add to both sides of the equation.
Step 3.3.3
Combine the opposite terms in .
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Step 3.3.3.1
Subtract from .
Step 3.3.3.2
Add and .
Step 3.3.3.3
Add and .
Step 3.3.3.4
Add and .
Step 3.4
Since , the equation will always be true for any value of .
All real numbers
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: