I've been trying to figure out this equation for over an hour but all the answers I get are wrong. The equation is 0.9=-10I^2+6I . The answer is supposed to be 0.3 and it does work out, but I have tried all different ways to solve for I and nothing seems to work. Could someone please help me?
I assume you know how to complete the square
-10 x^2 + 6 x = 0.9
x^2 -.6 x = -0.09
x^2 -.6 x + .09 = -.09+.09 = 0
(x-.3)^2 = 0
x = .3 sure enough.
x^2 -.6 x = -0.09 or just rearrange and factor
x^2 - .6 x + 0.09 = 0
(x-.3)(x-.3) = 0
x = .3 and x = .3
oh, okay, I see what you're doing. I just have one question, though;why is it that when you get rid of the -10, the 6 is affected by it? I would assume that it would be left alone...
oh, I forgot to thank you, so thank you very much!
oh, that makes it so much easier! Thank you so very much, it all makes sense now! :D
Or use quadratic equation
-10 x^2 + 6 x = 0.9
-10 x^2 + 6 x -.9 = 0
a = -10
b = 6
c = -.9
x = [-6 +/- sqrt (36-36) ]/-20
=-6/-20
=-3/-10
= 0.3
I divided both sides of the equation - ALL TERMS by -10
-10 x^2 + 6 x
---------------
-10
= x^2 -.6 x
oh, no wonder nothing worked out; thanks!
Of course, I'll be happy to help you solve the equation. The first step is to rearrange the equation to put it in the form of a quadratic equation, which is easier to solve. Let's start by combining like terms and moving all terms to one side of the equation:
-10I^2 + 6I + 0.9 = 0
Next, we can multiply the entire equation by -10 to eliminate the coefficient in front of the squared term:
100I^2 - 60I - 9 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 100, b = -60, and c = -9. To solve it, we can use the quadratic formula:
I = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
I = (-(-60) ± √((-60)^2 - 4(100)(-9))) / (2(100))
I = (60 ± √(3600 + 3600)) / 200
I = (60 ± √(7200)) / 200
I = (60 ± 84.85) / 200
Calculating the two roots, we get:
I1 = (60 + 84.85) / 200 ≈ 0.725
I2 = (60 - 84.85) / 200 ≈ -0.125
So, it seems like neither of these solutions matches your desired answer of 0.3. It's possible that there might have been a mistake made in the equation or the intended solution. Double-checking the equation and any additional information provided could help in finding the correct solution.