Basic Math Examples

Solve for z 7^(z^2)-49^(6-2z)=0
Step 1
Move to the right side of the equation by adding it to both sides.
Step 2
Create equivalent expressions in the equation that all have equal bases.
Step 3
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 4
Solve for .
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Step 4.1
Simplify .
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Step 4.1.1
Apply the distributive property.
Step 4.1.2
Multiply.
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Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Multiply by .
Step 4.2
Add to both sides of the equation.
Step 4.3
Subtract from both sides of the equation.
Step 4.4
Factor using the AC method.
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Step 4.4.1
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 4.4.2
Write the factored form using these integers.
Step 4.5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.6
Set equal to and solve for .
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Step 4.6.1
Set equal to .
Step 4.6.2
Add to both sides of the equation.
Step 4.7
Set equal to and solve for .
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Step 4.7.1
Set equal to .
Step 4.7.2
Subtract from both sides of the equation.
Step 4.8
The final solution is all the values that make true.