40-2q+.03q^2=40-q-.01q^2
.04q=1
q=25 this is what i keep getting but I am suppose to be getting 50 what am I doing wrong?
To solve the equation 40 - 2q + 0.03q^2 = 40 - q - 0.01q^2, you need to combine like terms and simplify the equation.
Step 1: Distribute the negative sign:
40 - 2q + 0.03q^2 = 40 - q - 0.01q^2
40 - 2q + 0.03q^2 = 40 - q + (-0.01q^2)
Step 2: Combine like terms:
0.03q^2 + (-0.01q^2) = 0.02q^2
40 - 2q = 40 - q
Step 3: Move all terms to one side of the equation:
0.02q^2 + 2q - q = 0
0.02q^2 + q = 0
Step 4: Multiply the equation by 100 to remove the decimal:
100 * (0.02q^2 + q) = 100 * 0
2q^2 + 100q = 0
Step 5: Factor out q from both terms:
q(2q + 100) = 0
Step 6: Set each factor equal to zero and solve for q:
q = 0 or 2q + 100 = 0
For q = 0:
Substituting q = 0 into the original equation will result in 40 - 2(0) + 0.03(0^2) = 40 - 0 - 0 = 40 which is a correct solution.
For 2q + 100 = 0:
Subtract 100 from both sides of the equation:
2q + 100 - 100 = 0 - 100
2q = -100
Divide both sides by 2:
2q / 2 = -100 / 2
q = -50 which is another solution.
Therefore, the correct solutions to the equation are q = 0 and q = -50, not q = 25 or q = 50 as you were expecting. It seems there may have been an error during your calculations.