# Solve for q 8q(q-10)+7=-42-q(q+38) 8q(q-10)+7=-42-q(q+38)
Simplify each term.
Apply the distributive property.
8q⋅q+8q⋅-10+7=-42-q(q+38)
Multiply q by q by adding the exponents.
Move q.
8(q⋅q)+8q⋅-10+7=-42-q(q+38)
Multiply q by q.
8q2+8q⋅-10+7=-42-q(q+38)
8q2+8q⋅-10+7=-42-q(q+38)
Multiply -10 by 8.
8q2-80q+7=-42-q(q+38)
8q2-80q+7=-42-q(q+38)
Simplify each term.
Apply the distributive property.
8q2-80q+7=-42-q⋅q-q⋅38
Multiply q by q by adding the exponents.
Move q.
8q2-80q+7=-42-(q⋅q)-q⋅38
Multiply q by q.
8q2-80q+7=-42-q2-q⋅38
8q2-80q+7=-42-q2-q⋅38
Multiply 38 by -1.
8q2-80q+7=-42-q2-38q
8q2-80q+7=-42-q2-38q
Move all terms containing q to the left side of the equation.
Add q2 to both sides of the equation.
8q2-80q+7+q2=-42-38q
Add 38q to both sides of the equation.
8q2-80q+7+q2+38q=-42
9q2-80q+7+38q=-42
9q2-42q+7=-42
9q2-42q+7=-42
Move 42 to the left side of the equation by adding it to both sides.
9q2-42q+7+42=0
9q2-42q+49=0
Factor using the perfect square rule.
Rewrite 9q2 as (3q)2.
(3q)2-42q+49=0
Rewrite 49 as 72.
(3q)2-42q+72=0
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅(3q)⋅-7
Simplify.
2ab=-42q
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=3q and b=-7.
(3q-7)2=0
(3q-7)2=0
Set the 3q-7 equal to 0.
3q-7=0
Solve for q.
Add 7 to both sides of the equation.
3q=7
Divide each term by 3 and simplify.
Divide each term in 3q=7 by 3.
3q3=73
Cancel the common factor of 3.
Cancel the common factor.
3q3=73
Divide q by 1.
q=73
q=73
q=73
q=73
The result can be shown in multiple forms.
Exact Form:
q=73
Decimal Form:
q=2.3‾
Mixed Number Form:
q=213
Solve for q 8q(q-10)+7=-42-q(q+38)

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