12pqx^2-(9p^2 -8q^2)x-6pq=0 full solution please guys
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STEP
1
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Equation at the end of step 1
((12pq•(x2))-(((9•(p2))-23q2)•x))-6pq = 0
STEP
2
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Equation at the end of step
2
:
((12pq•(x2))-((32p2-23q2)•x))-6pq = 0
STEP
3
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Trying to factor as a Difference of Squares
3.1 Factoring: 9p2-8q2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 8 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
3
:
((12pq • (x2)) - x • (9p2 - 8q2)) - 6pq = 0
STEP
4
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Equation at the end of step
4
:
((22•3pqx2) - x • (9p2 - 8q2)) - 6pq = 0
STEP
5
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Equation at the end of step 5
-9p2x + 12pqx2 - 6pq + 8q2x = 0
STEP
6
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Solving a Single Variable Equation
6.1 Solve -9p2x+12pqx2-6pq+8q2x = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
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