Basic Math Examples

Solve for q 8q(q-10)+7=-42-q(q+38)
Step 1
Simplify each term.
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Step 1.1
Apply the distributive property.
Step 1.2
Multiply by by adding the exponents.
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Step 1.2.1
Move .
Step 1.2.2
Multiply by .
Step 1.3
Multiply by .
Step 2
Simplify each term.
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Step 2.1
Apply the distributive property.
Step 2.2
Multiply by by adding the exponents.
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Step 2.2.1
Move .
Step 2.2.2
Multiply by .
Step 2.3
Multiply by .
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Add to both sides of the equation.
Step 3.2
Add to both sides of the equation.
Step 3.3
Add and .
Step 3.4
Add and .
Step 4
Add to both sides of the equation.
Step 5
Add and .
Step 6
Factor using the perfect square rule.
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Step 6.1
Rewrite as .
Step 6.2
Rewrite as .
Step 6.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 6.4
Rewrite the polynomial.
Step 6.5
Factor using the perfect square trinomial rule , where and .
Step 7
Set the equal to .
Step 8
Solve for .
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Step 8.1
Add to both sides of the equation.
Step 8.2
Divide each term in by and simplify.
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Step 8.2.1
Divide each term in by .
Step 8.2.2
Simplify the left side.
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Step 8.2.2.1
Cancel the common factor of .
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Step 8.2.2.1.1
Cancel the common factor.
Step 8.2.2.1.2
Divide by .
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: