Pre-Algebra Examples

Solve Using the Square Root Property x(27-x)=170
Step 1
Simplify .
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Step 1.1
Simplify by multiplying through.
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Step 1.1.1
Apply the distributive property.
Step 1.1.2
Reorder.
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Step 1.1.2.1
Move to the left of .
Step 1.1.2.2
Rewrite using the commutative property of multiplication.
Step 1.2
Multiply by by adding the exponents.
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Step 1.2.1
Move .
Step 1.2.2
Multiply by .
Step 2
Subtract from both sides of the equation.
Step 3
Factor the left side of the equation.
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Step 3.1
Factor out of .
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Step 3.1.1
Reorder and .
Step 3.1.2
Factor out of .
Step 3.1.3
Factor out of .
Step 3.1.4
Rewrite as .
Step 3.1.5
Factor out of .
Step 3.1.6
Factor out of .
Step 3.2
Factor.
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Step 3.2.1
Factor using the AC method.
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Step 3.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2.1.2
Write the factored form using these integers.
Step 3.2.2
Remove unnecessary parentheses.
Step 4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Add to both sides of the equation.
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Add to both sides of the equation.
Step 7
The final solution is all the values that make true.