(-7w^2=2w-1)-(-5w^2+3w-2)
Starting with (-7w^2=2w-1), we can simplify by adding 5w^2 to both sides and by adding 1 to both sides:
-7w^2 + 5w^2 = 2w - 1 + 1
Simplifying further, we get:
-2w^2 = 2w
Dividing both sides by -2w, we get:
w = 0 or w = -1
Now, starting with (-5w^2+3w-2), we can simplify by subtracting 2 from both sides:
-5w^2 + 3w - 2 + 2 = 0
Simplifying further, we get:
-5w^2 + 3w = 0
Factoring out w, we get:
w(-5w + 3) = 0
So w = 0 or w = 3/5
Putting it all together, we have:
(-7w^2=2w-1)-(-5w^2+3w-2)
= (-7w^2+5w^2) - (2w-3w) - (1+2)
= -2w^2 - w - 3
Now, plugging in our values for w, we get:
w = 0 -> -2(0)^2 - (0) - 3 = -3
w = -1 -> -2(-1)^2 - (-1) - 3 = -4
w = 3/5 -> -2(3/5)^2 - (3/5) - 3 = -4.68 (rounded to two decimal places)
Therefore, our final answer is:
(-7w^2=2w-1)-(-5w^2+3w-2) = {-3 if w = 0, -4 if w = -1, -4.68 if w = 3/5}
(-7w^2=2w-1)-(-5w^2+3w-2)
12w^2+5w+1
-2w^2-5w-1
-2w^2-5w+1
-12w^2-5w-3
The correct answer is:
-2w^2-5w-1
To simplify the expression (-7w^2=2w-1) - (-5w^2+3w-2), you need to follow a few steps:
Step 1: Distribute the negative sign (-) to each term within the second parentheses:
(-7w^2 = 2w - 1) - (-5w^2 + 3w - 2)
becomes:
-7w^2 = 2w - 1 + 5w^2 - 3w + 2
Step 2: Combine like terms:
-7w^2 + 5w^2 = 2w + 5w^2 - 3w - 1 + 2
-2w^2 = 2w + 5w^2 - 3w + 1
Step 3: Rearrange the equation by moving all terms to one side to make it equal to zero:
-2w^2 - 2w - 5w^2 + 3w + 1 = 0
Step 4: Combine like terms:
(-2w^2 - 5w^2) + (-2w + 3w) + 1 = 0
-7w^2 + w + 1 = 0
And that is the simplified form of the expression (-7w^2=2w-1) - (-5w^2+3w-2).