What number makes this equation TRUE?
q2 + 3q - 18 = (q + 6)(q - _)
the left side factors to
(q+6)(q-3)
To find the missing number in the equation (q + 6)(q - _), we need to simplify the equation on the right side and then compare it to the left side of the equation.
Expanding the equation (q + 6)(q - _), we have:
(q + 6)(q - _) = q^2 + 6q - _q - 6_
Combining like terms, the equation becomes:
q^2 + 6q - _q - 6_ = q^2 + 3q - 18
To find the missing number, we can compare the coefficients of the terms on both sides:
On the left side, the coefficient of q is (6 - _), which can be simplified to 6 - _.
On the right side, the coefficient of q is 3.
Setting these coefficients equal to each other:
6 - _ = 3
Solving for _, we subtract 3 from both sides:
6 - 3 = _
Therefore, the missing number in the equation is 3.
To find the number that makes the equation true, we need to determine the value of the missing term in the equation.
Let's first expand the right-hand side of the equation:
(q + 6)(q - _)
= q * q + q * (-_) + 6 * q + 6 * (-_)
Combining like terms, we get:
= q^2 - _q + 6q - 6_
Next, let's set this expression equal to the left-hand side of the equation:
q^2 - _q + 6q - 6_ = q^2 + 3q - 18
Now, we can compare the corresponding terms on both sides:
-q + 6q = 3q
-6_ = -18
From the first comparison, we can conclude that -q + 6q = 3q. Simplifying this equation gives us q = 3q.
To solve for q, we can cancel out the "q" term on both sides of the equation by subtracting 3q from both sides:
q - 3q = 0
-2q = 0
Dividing both sides by -2, we find:
q = 0
Now that we have determined the value of q, we can substitute it back into the equation to find the missing term:
q^2 - _q + 6q - 6_ = q^2 + 3q - 18
Substituting q = 0 gives us:
0^2 - _ * 0 + 6 * 0 - 6_ = 0^2 + 3 * 0 - 18
This simplifies to:
0 + 0 - 6_ = 0 - 18
To make the equation true, the missing term should be -12, making the equation:
q^2 - 12q + 6q - 72 = q^2 + 3q - 18