Finite Math Examples

Solve by Factoring square root of x^2-10x+25+12 square root of x=15 square root of x
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Factor using the perfect square rule.
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Step 2.1.1.1
Rewrite as .
Step 2.1.1.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.1.1.3
Rewrite the polynomial.
Step 2.1.1.4
Factor using the perfect square trinomial rule , where and .
Step 2.1.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2
Subtract from .
Step 3
Move all terms not containing to the right side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Add to both sides of the equation.
Step 4
To remove the radical on the left side of the equation, square both sides of the equation.
Step 5
Simplify each side of the equation.
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Step 5.1
Use to rewrite as .
Step 5.2
Simplify the left side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Apply the product rule to .
Step 5.2.1.2
Raise to the power of .
Step 5.2.1.3
Multiply the exponents in .
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Step 5.2.1.3.1
Apply the power rule and multiply exponents, .
Step 5.2.1.3.2
Cancel the common factor of .
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Step 5.2.1.3.2.1
Cancel the common factor.
Step 5.2.1.3.2.2
Rewrite the expression.
Step 5.2.1.4
Simplify.
Step 5.3
Simplify the right side.
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Step 5.3.1
Simplify .
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Step 5.3.1.1
Rewrite as .
Step 5.3.1.2
Expand using the FOIL Method.
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Step 5.3.1.2.1
Apply the distributive property.
Step 5.3.1.2.2
Apply the distributive property.
Step 5.3.1.2.3
Apply the distributive property.
Step 5.3.1.3
Simplify and combine like terms.
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Step 5.3.1.3.1
Simplify each term.
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Step 5.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 5.3.1.3.1.2
Multiply by by adding the exponents.
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Step 5.3.1.3.1.2.1
Move .
Step 5.3.1.3.1.2.2
Multiply by .
Step 5.3.1.3.1.3
Multiply by .
Step 5.3.1.3.1.4
Multiply by .
Step 5.3.1.3.1.5
Multiply by .
Step 5.3.1.3.1.6
Multiply by .
Step 5.3.1.3.1.7
Multiply by .
Step 5.3.1.3.2
Subtract from .
Step 6
Solve for .
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Step 6.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 6.2
Move all terms containing to the left side of the equation.
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Step 6.2.1
Subtract from both sides of the equation.
Step 6.2.2
Subtract from .
Step 6.3
Use the quadratic formula to find the solutions.
Step 6.4
Substitute the values , , and into the quadratic formula and solve for .
Step 6.5
Simplify.
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Step 6.5.1
Simplify the numerator.
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Step 6.5.1.1
Raise to the power of .
Step 6.5.1.2
Multiply .
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Step 6.5.1.2.1
Multiply by .
Step 6.5.1.2.2
Multiply by .
Step 6.5.1.3
Subtract from .
Step 6.5.1.4
Rewrite as .
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Step 6.5.1.4.1
Factor out of .
Step 6.5.1.4.2
Rewrite as .
Step 6.5.1.5
Pull terms out from under the radical.
Step 6.5.2
Multiply by .
Step 6.6
Simplify the expression to solve for the portion of the .
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Step 6.6.1
Simplify the numerator.
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Step 6.6.1.1
Raise to the power of .
Step 6.6.1.2
Multiply .
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Step 6.6.1.2.1
Multiply by .
Step 6.6.1.2.2
Multiply by .
Step 6.6.1.3
Subtract from .
Step 6.6.1.4
Rewrite as .
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Step 6.6.1.4.1
Factor out of .
Step 6.6.1.4.2
Rewrite as .
Step 6.6.1.5
Pull terms out from under the radical.
Step 6.6.2
Multiply by .
Step 6.6.3
Change the to .
Step 6.7
Simplify the expression to solve for the portion of the .
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Step 6.7.1
Simplify the numerator.
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Step 6.7.1.1
Raise to the power of .
Step 6.7.1.2
Multiply .
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Step 6.7.1.2.1
Multiply by .
Step 6.7.1.2.2
Multiply by .
Step 6.7.1.3
Subtract from .
Step 6.7.1.4
Rewrite as .
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Step 6.7.1.4.1
Factor out of .
Step 6.7.1.4.2
Rewrite as .
Step 6.7.1.5
Pull terms out from under the radical.
Step 6.7.2
Multiply by .
Step 6.7.3
Change the to .
Step 6.8
The final answer is the combination of both solutions.
Step 7
Exclude the solutions that do not make true.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: