How do you solve #x^2+6x+9=-32#?
The left hand side here is a perfect square trinomial, but the right hand side is negative, so only has an imaginary square root.
We find:
Hence:
So:
By signing up, you agree to our Terms of Service and Privacy Policy
To solve the equation (x^2 + 6x + 9 = -32), follow these steps:
-
Start by adding 32 to both sides of the equation to move all terms to one side: [x^2 + 6x + 9 + 32 = 0] [x^2 + 6x + 41 = 0]
-
Now, use the quadratic formula to find the solutions for (x): [x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]
For the equation (ax^2 + bx + c = 0), in our case, (a = 1), (b = 6), and (c = 41).
-
Plug in the values into the quadratic formula: [x = \frac{{-6 \pm \sqrt{{6^2 - 4(1)(41)}}}}{{2(1)}}]
-
Simplify under the square root: [x = \frac{{-6 \pm \sqrt{{36 - 164}}}}{2}] [x = \frac{{-6 \pm \sqrt{{-128}}}}{2}] [x = \frac{{-6 \pm 8i\sqrt{2}}}{2}]
-
Split into two solutions, one with the plus sign and one with the minus sign: [x = \frac{{-6 + 8i\sqrt{2}}}{2}] [x = \frac{{-6 - 8i\sqrt{2}}}{2}]
So, the solutions for (x) are: [x = -3 + 4i\sqrt{2}] [x = -3 - 4i\sqrt{2}]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you find the vertex for #y=x^2-4#?
- How do you find the intercepts and vertex for #f(x)= 3x^2+x-5#?
- How do you find the vertex and the intercepts for #y = x^2 - 4x#?
- What is the vertex of # y= x^2 -9 - 8x#?
- If the quadratic equation can be used to determine when a function equals zero, is there a modified quadratic equation that can determine when a function equals another constant?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7