Hello,
I'm a little confused & not sure where I went wrong:
Solve the following systems of equations algebraically using the quadratic formula. Round answer to 2 decimal places.
y=-x^2+2x+9
y=-5x^2+10x+12
My work:
-x^2+2x+9=-5x+10x+12
Move everything from the right side to the left
4x^2-8x+7=0
x=(8+/- Root (64-4(4)(7)))/ 2(4)
My problem is that 64-4*4*7 is a negative number... Which makes me think I've made a wrong turn somewhere.
Thanks a bunch for your help! :)
-x^2+2x+9=-5x+10x+12
you mean
-x^2+2x+9=-5x^2 +10x+12 I am sure
whoops
9 - 12 = -3 not 7
4x^2-8x-3=0
[ 8 +/- sqrt 112 ]/8
I get 1 +/- .5 sqrt 7
Oh gosh! I dropped the 1 in 12... that's my whole problem. Thank you so much!
Hello!
I understand that you are trying to solve the system of equations algebraically using the quadratic formula. Let's go through the process step by step to find where you may have made a mistake.
To solve the system of equations, we need to set the two equations equal to each other, like you did:
-x^2 + 2x + 9 = -5x^2 + 10x + 12
Next, we want to rearrange the equation in standard quadratic form, which means collecting all the terms on one side to set it equal to zero. You correctly moved everything from the right side to the left side:
4x^2 - 8x + 7 = 0
Now, to use the quadratic formula, we need to identify the coefficients a, b, and c from the quadratic equation ax^2 + bx + c = 0. In this case, a = 4, b = -8, and c = 7.
Using the quadratic formula, which is x = (-b +/- sqrt(b^2 - 4ac)) / (2a), we can substitute these values into the formula:
x = (-(-8) +/- sqrt((-8)^2 - 4 * 4 * 7)) / (2 * 4)
Simplifying further:
x = (8 +/- sqrt(64 - 112)) / 8
And now, we have found where you made a mistake. When you evaluated the discriminant, which is the expression inside the square root, you obtained a negative number. This means that the quadratic equation does not have any real solutions.
In this case, the system of equations does not have any solutions that can be found using the quadratic formula. You may want to check if there might be an error in the original equations or if there is a different method you can use to solve the system.
I hope this helps clarify where the mistake occurred. If you have any further questions, feel free to ask!