Use the quadratic formula to solve. Express your answer in simplest form.
minus, 3, r, squared, plus, 9, r, plus, 4, equals, minus, 5, r, squared
−3r
2
+9r+4=
−5r
2
To solve the given equation using the quadratic formula, let's first rearrange the equation to have all terms on one side:
-3r^2 + 9r + 4 = -5r^2
Now, let's bring all terms to one side:
0 = -5r^2 + 3r^2 - 9r - 4
Next, let's combine like terms:
0 = -2r^2 - 9r - 4
Now we can apply the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions (x-values) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -2, b = -9, and c = -4.
Plugging these values into the quadratic formula, we get:
r = (-(-9) ± √((-9)^2 - 4(-2)(-4))) / (2(-2))
Simplifying, we get:
r = (9 ± √(81 - 32)) / (-4)
r = (9 ± √49) / (-4)
r = (9 ± 7) / (-4)
Now we can find the two possible values of r by evaluating the expression with both the plus and minus signs:
1) r = (9 + 7) / (-4) = 16 / (-4) = -4
2) r = (9 - 7) / (-4) = 2 / (-4) = -1/2
Therefore, the solutions to the equation are r = -4 and r = -1/2.