We appreciate your visit to Rewrite the equation in the form tex x p 2 q tex Given equation tex x 2 20x 98 5 0 tex The rewritten equation. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To rewrite the equation [tex]\(x^2 + 20x + 98.5 = 0\)[/tex] in the form [tex]\((x-p)^2 = q\)[/tex], we will follow these steps:
1. Move the constant term to the other side: Start by isolating the quadratic and linear terms on one side.
[tex]\[
x^2 + 20x = -98.5
\][/tex]
2. Complete the square: We will add a number to both sides to make the left-hand side a perfect square trinomial. To do this, take half of the coefficient of [tex]\(x\)[/tex], square it, and add to both sides.
[tex]\[
\text{Coefficient of } x = 20 \quad \Rightarrow \quad \frac{20}{2} = 10
\][/tex]
[tex]\[
10^2 = 100
\][/tex]
Add 100 to both sides of the equation:
[tex]\[
x^2 + 20x + 100 = -98.5 + 100
\][/tex]
Simplifying the right side gives:
[tex]\[
x^2 + 20x + 100 = 1.5
\][/tex]
3. Factor the perfect square trinomial: The left-hand side is now a perfect square trinomial, which factors as:
[tex]\[
(x + 10)^2 = 1.5
\][/tex]
In conclusion, the equation rewritten in the form [tex]\((x-p)^2 = q\)[/tex] is:
[tex]\[
(x + 10)^2 = 1.5
\][/tex]
1. Move the constant term to the other side: Start by isolating the quadratic and linear terms on one side.
[tex]\[
x^2 + 20x = -98.5
\][/tex]
2. Complete the square: We will add a number to both sides to make the left-hand side a perfect square trinomial. To do this, take half of the coefficient of [tex]\(x\)[/tex], square it, and add to both sides.
[tex]\[
\text{Coefficient of } x = 20 \quad \Rightarrow \quad \frac{20}{2} = 10
\][/tex]
[tex]\[
10^2 = 100
\][/tex]
Add 100 to both sides of the equation:
[tex]\[
x^2 + 20x + 100 = -98.5 + 100
\][/tex]
Simplifying the right side gives:
[tex]\[
x^2 + 20x + 100 = 1.5
\][/tex]
3. Factor the perfect square trinomial: The left-hand side is now a perfect square trinomial, which factors as:
[tex]\[
(x + 10)^2 = 1.5
\][/tex]
In conclusion, the equation rewritten in the form [tex]\((x-p)^2 = q\)[/tex] is:
[tex]\[
(x + 10)^2 = 1.5
\][/tex]
Thanks for taking the time to read Rewrite the equation in the form tex x p 2 q tex Given equation tex x 2 20x 98 5 0 tex The rewritten equation. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
