At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To solve for [tex]\(x\)[/tex] in the quadratic equation using the quadratic formula, we need to evaluate the expression:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Given [tex]\(a = 1\)[/tex], [tex]\(b = -2\)[/tex], and [tex]\(c = -8\)[/tex], the first step is to calculate the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[ \text{Discriminant} = (-2)^2 - 4(1)(-8) \][/tex]
Calculating inside the discriminant:
[tex]\[ \text{Discriminant} = 4 + 32 = 36 \][/tex]
Next, we find the square root of the discriminant:
[tex]\[ \sqrt{36} = 6 \][/tex]
Now, we substitute back into the quadratic formula:
[tex]\[ x = \frac{-(-2) \pm \sqrt{36}}{2(1)} \][/tex]
Simplify the expressions:
[tex]\[ x = \frac{2 \pm 6}{2} \][/tex]
Therefore, the number needed for our problem is 6, because:
[tex]\[ x = \frac{2 \pm [?]}{[]} \][/tex]
We find that [tex]\( \pm ? = 6 \)[/tex].
So, the number that belongs in the green box is:
[tex]\[ \boxed{6} \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Given [tex]\(a = 1\)[/tex], [tex]\(b = -2\)[/tex], and [tex]\(c = -8\)[/tex], the first step is to calculate the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[ \text{Discriminant} = (-2)^2 - 4(1)(-8) \][/tex]
Calculating inside the discriminant:
[tex]\[ \text{Discriminant} = 4 + 32 = 36 \][/tex]
Next, we find the square root of the discriminant:
[tex]\[ \sqrt{36} = 6 \][/tex]
Now, we substitute back into the quadratic formula:
[tex]\[ x = \frac{-(-2) \pm \sqrt{36}}{2(1)} \][/tex]
Simplify the expressions:
[tex]\[ x = \frac{2 \pm 6}{2} \][/tex]
Therefore, the number needed for our problem is 6, because:
[tex]\[ x = \frac{2 \pm [?]}{[]} \][/tex]
We find that [tex]\( \pm ? = 6 \)[/tex].
So, the number that belongs in the green box is:
[tex]\[ \boxed{6} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.