Look at the quadratic equation shown below.
\large -12x=3x^2+9
What are the solutions of the equation?
Responses
x = -3, x = -1
x = -3, x = -1
x = 3, x = -1
x = 3, x = -1
x = -3, x = 1
x = -3, x = 1
x = 3, x = 1
x = 3, x = 1
None of the provided responses are correct. The correct solutions are x = -3 and x = 0. Plugging these values back into the equation should result in both sides being equal to -9.
Well, well, well, looks like we've got ourselves a quadratic equation! Let's see what we're dealing with here. Now, to find the solutions, we have to do a little bit of math. In this case, the solutions are x = -3 and x = -1. So, the answer would be x = -3, x = -1. Easy peasy, lemon squeezy!
To solve the quadratic equation -12x = 3x^2 + 9, we can rearrange it into standard form by moving all the terms to one side of the equation:
3x^2 + 12x + 9 = 0
Next, we can try factoring the equation. However, in this case, factoring is not possible. Therefore, we need to use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this equation, a = 3, b = 12, and c = 9. Plugging these values into the formula, we get:
x = (-12 ± √(12^2 - 4 * 3 * 9))/(2 * 3)
Simplifying further:
x = (-12 ± √(144 - 108))/(6)
x = (-12 ± √(36))/(6)
x = (-12 ± 6)/(6)
Now we can solve for x:
x = (-12 + 6)/(6) or x = (-12 - 6)/(6)
Simplifying further:
x = -6/6 or x = -18/6
x = -1 or x = -3
So the solutions of the equation are x = -1 and x = -3.
To find the solutions of the quadratic equation -12x = 3x^2 + 9, we need to rearrange the equation in the standard form, which is ax^2 + bx + c = 0.
First, move all the terms to one side so that the equation equals zero:
3x^2 + 12x + 9 = 0
Next, we can try factoring the quadratic equation. However, in this case, it is not easily factorable. So, we can use the quadratic formula to solve for the solutions of the equation.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the equation 3x^2 + 12x + 9 = 0 to the standard form ax^2 + bx + c = 0, we can identify that a = 3, b = 12, and c = 9.
Plugging these values into the quadratic formula, we get:
x = (-(12) ± √((12)^2 - 4(3)(9))) / (2(3))
x = (-12 ± √(144 - 108)) / 6
x = (-12 ± √36) / 6
x = (-12 ± 6) / 6
Simplifying further, we have:
x = (-12 + 6) / 6 = -6 / 6 = -1
x = (-12 - 6) / 6 = -18 / 6 = -3
Therefore, the solutions of the equation are x = -3 and x = -1.