Pre-Algebra Examples

Solve Using the Square Root Property 2k(k+15)=15
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Simplify the expression.
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Step 1.2.3.1
Multiply by .
Step 1.2.3.2
Move to the left of .
Step 2
Subtract from both sides of the equation.
Step 3
Multiply through by the least common denominator , then simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Simplify.
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Step 3.2.1
Multiply by .
Step 3.2.2
Cancel the common factor of .
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Step 3.2.2.1
Move the leading negative in into the numerator.
Step 3.2.2.2
Cancel the common factor.
Step 3.2.2.3
Rewrite the expression.
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
Add and .
Step 6.1.4
Rewrite as .
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Step 6.1.4.1
Factor out of .
Step 6.1.4.2
Rewrite as .
Step 6.1.5
Pull terms out from under the radical.
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
Add and .
Step 7.1.4
Rewrite as .
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Step 7.1.4.1
Factor out of .
Step 7.1.4.2
Rewrite as .
Step 7.1.5
Pull terms out from under the radical.
Step 7.2
Multiply by .
Step 7.3
Simplify .
Step 7.4
Change the to .
Step 7.5
Rewrite as .
Step 7.6
Factor out of .
Step 7.7
Factor out of .
Step 7.8
Move the negative in front of the fraction.
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
Add and .
Step 8.1.4
Rewrite as .
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Step 8.1.4.1
Factor out of .
Step 8.1.4.2
Rewrite as .
Step 8.1.5
Pull terms out from under the radical.
Step 8.2
Multiply by .
Step 8.3
Simplify .
Step 8.4
Change the to .
Step 8.5
Rewrite as .
Step 8.6
Factor out of .
Step 8.7
Factor out of .
Step 8.8
Move the negative in front of the fraction.
Step 9
The final answer is the combination of both solutions.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: