Math  /  Algebra

QuestionSolve using the quadratic formula. 7d2+4d=07 d^{2}+4 d=0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

Studdy Solution

STEP 1

What is this asking? We need to find the values of dd that make the equation 7d2+4d=07d^2 + 4d = 0 true, and we're told to use the quadratic formula! Watch out! Remember, the quadratic formula is a powerful tool, but make sure you identify your aa, bb, and cc correctly before plugging them in!
Also, don't forget to simplify your answers!

STEP 2

1. Set up the equation
2. Apply the quadratic formula
3. Simplify the solutions

STEP 3

Alright, so we've got our equation 7d2+4d=07d^2 + 4d = 0.
We want it in the standard form ax2+bx+c=0ax^2 + bx + c = 0 to use the quadratic formula.
Luckily, it's practically already there!

STEP 4

We can see that our **aa is 77**, our **bb is 44**, and our **cc is 00**.
See how the constant term is missing?
That just means cc is zero!

STEP 5

Remember, the quadratic formula is: x=b±b24ac2a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} Let's plug in our **aa, bb, and cc values**.

STEP 6

Substituting, we get: d=4±4247027 d = \frac{-4 \pm \sqrt{4^2 - 4 \cdot 7 \cdot 0}}{2 \cdot 7}

STEP 7

Let's simplify that square root first. 424^2 is **1616**, and anything multiplied by zero is zero, so the whole thing under the square root simplifies to just **1616**!
The square root of 1616 is **44**.
So we have: d=4±414 d = \frac{-4 \pm 4}{14}

STEP 8

Now, we have two possible solutions: one with the plus sign and one with the minus sign.
Let's do the plus sign first: d=4+414=014=0 d = \frac{-4 + 4}{14} = \frac{0}{14} = 0 So, one solution is d=0d = 0!

STEP 9

Now for the minus sign: d=4414=814 d = \frac{-4 - 4}{14} = \frac{-8}{14} We can simplify this fraction by dividing the top and bottom by 22, which gives us d=47d = \frac{-4}{7}.

STEP 10

Our solutions are d=0d = 0 and d=47d = \frac{-4}{7}.
Awesome!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord