Pre-Algebra Examples

Solve Using the Square Root Property -x^2-10x-21=x^2+12x+27
Step 1
Move all terms containing to the left side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Subtract from .
Step 1.4
Subtract from .
Step 2
Subtract from both sides of the equation.
Step 3
Subtract from .
Step 4
Factor the left side of the equation.
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Step 4.1
Factor out of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Factor out of .
Step 4.1.3
Factor out of .
Step 4.1.4
Factor out of .
Step 4.1.5
Factor out of .
Step 4.2
Factor.
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Step 4.2.1
Factor using the AC method.
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Step 4.2.1.1
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 4.2.1.2
Write the factored form using these integers.
Step 4.2.2
Remove unnecessary parentheses.
Step 5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Subtract from both sides of the equation.
Step 7
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Subtract from both sides of the equation.
Step 8
The final solution is all the values that make true.