Basic Math Examples

Solve for d 3 square root of 2d-3+2 square root of 7-d=11
Step 1
Subtract from both sides of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Simplify each side of the equation.
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Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Apply the product rule to .
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Multiply the exponents in .
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Step 3.2.1.3.1
Apply the power rule and multiply exponents, .
Step 3.2.1.3.2
Cancel the common factor of .
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Step 3.2.1.3.2.1
Cancel the common factor.
Step 3.2.1.3.2.2
Rewrite the expression.
Step 3.2.1.4
Simplify.
Step 3.2.1.5
Apply the distributive property.
Step 3.2.1.6
Multiply.
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Step 3.2.1.6.1
Multiply by .
Step 3.2.1.6.2
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify .
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Step 3.3.1.1
Rewrite as .
Step 3.3.1.2
Expand using the FOIL Method.
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Step 3.3.1.2.1
Apply the distributive property.
Step 3.3.1.2.2
Apply the distributive property.
Step 3.3.1.2.3
Apply the distributive property.
Step 3.3.1.3
Simplify and combine like terms.
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Step 3.3.1.3.1
Simplify each term.
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Step 3.3.1.3.1.1
Multiply by .
Step 3.3.1.3.1.2
Multiply by .
Step 3.3.1.3.1.3
Multiply by .
Step 3.3.1.3.1.4
Multiply .
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Step 3.3.1.3.1.4.1
Multiply by .
Step 3.3.1.3.1.4.2
Raise to the power of .
Step 3.3.1.3.1.4.3
Raise to the power of .
Step 3.3.1.3.1.4.4
Use the power rule to combine exponents.
Step 3.3.1.3.1.4.5
Add and .
Step 3.3.1.3.1.5
Rewrite as .
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Step 3.3.1.3.1.5.1
Use to rewrite as .
Step 3.3.1.3.1.5.2
Apply the power rule and multiply exponents, .
Step 3.3.1.3.1.5.3
Combine and .
Step 3.3.1.3.1.5.4
Cancel the common factor of .
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Step 3.3.1.3.1.5.4.1
Cancel the common factor.
Step 3.3.1.3.1.5.4.2
Rewrite the expression.
Step 3.3.1.3.1.5.5
Simplify.
Step 3.3.1.3.1.6
Apply the distributive property.
Step 3.3.1.3.1.7
Multiply by .
Step 3.3.1.3.1.8
Multiply by .
Step 3.3.1.3.2
Add and .
Step 3.3.1.3.3
Subtract from .
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Add to both sides of the equation.
Step 4.2.3
Add and .
Step 4.2.4
Subtract from .
Step 5
To remove the radical on the left side of the equation, square both sides of the equation.
Step 6
Simplify each side of the equation.
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Step 6.1
Use to rewrite as .
Step 6.2
Simplify the left side.
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Step 6.2.1
Simplify .
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Step 6.2.1.1
Apply the product rule to .
Step 6.2.1.2
Raise to the power of .
Step 6.2.1.3
Multiply the exponents in .
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Step 6.2.1.3.1
Apply the power rule and multiply exponents, .
Step 6.2.1.3.2
Cancel the common factor of .
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Step 6.2.1.3.2.1
Cancel the common factor.
Step 6.2.1.3.2.2
Rewrite the expression.
Step 6.2.1.4
Simplify.
Step 6.2.1.5
Apply the distributive property.
Step 6.2.1.6
Multiply.
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Step 6.2.1.6.1
Multiply by .
Step 6.2.1.6.2
Multiply by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Simplify .
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Step 6.3.1.1
Rewrite as .
Step 6.3.1.2
Expand using the FOIL Method.
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Step 6.3.1.2.1
Apply the distributive property.
Step 6.3.1.2.2
Apply the distributive property.
Step 6.3.1.2.3
Apply the distributive property.
Step 6.3.1.3
Simplify and combine like terms.
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Step 6.3.1.3.1
Simplify each term.
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Step 6.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.2
Multiply by by adding the exponents.
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Step 6.3.1.3.1.2.1
Move .
Step 6.3.1.3.1.2.2
Multiply by .
Step 6.3.1.3.1.3
Multiply by .
Step 6.3.1.3.1.4
Multiply by .
Step 6.3.1.3.1.5
Multiply by .
Step 6.3.1.3.1.6
Multiply by .
Step 6.3.1.3.2
Subtract from .
Step 7
Solve for .
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Step 7.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 7.2
Move all terms containing to the left side of the equation.
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Step 7.2.1
Add to both sides of the equation.
Step 7.2.2
Add and .
Step 7.3
Subtract from both sides of the equation.
Step 7.4
Subtract from .
Step 7.5
Factor the left side of the equation.
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Step 7.5.1
Factor out of .
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Step 7.5.1.1
Factor out of .
Step 7.5.1.2
Factor out of .
Step 7.5.1.3
Factor out of .
Step 7.5.1.4
Factor out of .
Step 7.5.1.5
Factor out of .
Step 7.5.2
Factor using the perfect square rule.
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Step 7.5.2.1
Rewrite as .
Step 7.5.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 7.5.2.3
Rewrite the polynomial.
Step 7.5.2.4
Factor using the perfect square trinomial rule , where and .
Step 7.6
Divide each term in by and simplify.
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Step 7.6.1
Divide each term in by .
Step 7.6.2
Simplify the left side.
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Step 7.6.2.1
Cancel the common factor of .
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Step 7.6.2.1.1
Cancel the common factor.
Step 7.6.2.1.2
Divide by .
Step 7.6.3
Simplify the right side.
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Step 7.6.3.1
Divide by .
Step 7.7
Set the equal to .
Step 7.8
Add to both sides of the equation.