Pre-Algebra Examples

Solve Using the Square Root Property 2z^2-2z-143/2=0
Step 1
Multiply through by the least common denominator , then simplify.
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Step 1.1
Apply the distributive property.
Step 1.2
Simplify.
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Step 1.2.1
Multiply by .
Step 1.2.2
Multiply by .
Step 1.2.3
Cancel the common factor of .
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Step 1.2.3.1
Move the leading negative in into the numerator.
Step 1.2.3.2
Cancel the common factor.
Step 1.2.3.3
Rewrite the expression.
Step 2
Use the quadratic formula to find the solutions.
Step 3
Substitute the values , , and into the quadratic formula and solve for .
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Raise to the power of .
Step 4.1.2
Multiply .
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Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Multiply by .
Step 4.1.3
Add and .
Step 4.1.4
Rewrite as .
Step 4.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 4.2
Multiply by .
Step 4.3
Simplify .
Step 5
Simplify the expression to solve for the portion of the .
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Step 5.1
Simplify the numerator.
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Step 5.1.1
Raise to the power of .
Step 5.1.2
Multiply .
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Step 5.1.2.1
Multiply by .
Step 5.1.2.2
Multiply by .
Step 5.1.3
Add and .
Step 5.1.4
Rewrite as .
Step 5.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 5.2
Multiply by .
Step 5.3
Simplify .
Step 5.4
Change the to .
Step 5.5
Add and .
Step 6
Simplify the expression to solve for the portion of the .
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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
Add and .
Step 6.1.4
Rewrite as .
Step 6.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 6.4
Change the to .
Step 6.5
Subtract from .
Step 6.6
Move the negative in front of the fraction.
Step 7
The final answer is the combination of both solutions.