Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
-1 or 5/2
Step-by-step explanation:
The ratio in the question implies that, by cross-multiplying, x2⋅2=(3x+5)⋅1 , in other words 2x2=3x+5 . Therefore, 2x2−3x−5=0 .
There are many ways to try to solve this, one way is to factor: 2x2−3x−5=(x+1)(2x−5) , so the possible values of x are −1 and 52 .
Another way is to use the quadratic formula: x=−b±b2−4ac√2a=3±32+4⋅2⋅5√2⋅2=3±49√4=3±74 , which is either −1 or 52 .
Another way is completing the square:
2x2−3x−5=0
Dividing both sides by 2, x2−32x−52=0
Adding 52 to separate summands, x2−32x=52
Adding 916 to complete the square, x2−32x+916=52+916=4916
Factoring the left-hand side gives (x−34)2=4916 . Hence, taking square roots, x−34=±74 .
Moreover, x=34±74 , which is either −1 or 52 .
Another way is inverting the square:
2x2−3x−5=0⟹2x−5x=3
(2x−5x)2=9
4x2−20+25x2=9 (expand left-hand side)
4x2+20+25x2=49 (add 40 to both sides)
(2x+5x)2=49 (factor left-hand side)
2x+5x=±7
4x=(2x−5x)+(2x+5x)=3±7
x=3±74 , which is either −1 or 52 .
Another way is to graph; that strategy will be omitted here.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
