Pre-Algebra Examples

Solve Using the Square Root Property 8z^2-8z=-38
Step 1
Add to both sides of the equation.
Step 2
Factor out of .
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
Step 2.4
Factor out of .
Step 2.5
Factor out of .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Divide by .
Step 4
Use the quadratic formula to find the solutions.
Step 5
Substitute the values , , and into the quadratic formula and solve for .
Step 6
Simplify.
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Raise to the power of .
Step 6.1.2
Multiply .
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Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 6.1.3
Subtract from .
Step 6.1.4
Rewrite as .
Step 6.1.5
Rewrite as .
Step 6.1.6
Rewrite as .
Step 6.1.7
Rewrite as .
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Step 6.1.7.1
Factor out of .
Step 6.1.7.2
Rewrite as .
Step 6.1.8
Pull terms out from under the radical.
Step 6.1.9
Move to the left of .
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 7
Simplify the expression to solve for the portion of the .
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Step 7.1
Simplify the numerator.
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Step 7.1.1
Raise to the power of .
Step 7.1.2
Multiply .
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Step 7.1.2.1
Multiply by .
Step 7.1.2.2
Multiply by .
Step 7.1.3
Subtract from .
Step 7.1.4
Rewrite as .
Step 7.1.5
Rewrite as .
Step 7.1.6
Rewrite as .
Step 7.1.7
Rewrite as .
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Step 7.1.7.1
Factor out of .
Step 7.1.7.2
Rewrite as .
Step 7.1.8
Pull terms out from under the radical.
Step 7.1.9
Move to the left of .
Step 7.2
Multiply by .
Step 7.3
Simplify .
Step 7.4
Change the to .
Step 8
Simplify the expression to solve for the portion of the .
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Step 8.1
Simplify the numerator.
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Step 8.1.1
Raise to the power of .
Step 8.1.2
Multiply .
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Step 8.1.2.1
Multiply by .
Step 8.1.2.2
Multiply by .
Step 8.1.3
Subtract from .
Step 8.1.4
Rewrite as .
Step 8.1.5
Rewrite as .
Step 8.1.6
Rewrite as .
Step 8.1.7
Rewrite as .
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Step 8.1.7.1
Factor out of .
Step 8.1.7.2
Rewrite as .
Step 8.1.8
Pull terms out from under the radical.
Step 8.1.9
Move to the left of .
Step 8.2
Multiply by .
Step 8.3
Simplify .
Step 8.4
Change the to .
Step 9
The final answer is the combination of both solutions.