Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
To find the values of x:
Given equation: [tex](x+7)(x-9)=25[/tex]
Then: [tex]x(x-9)+7(x-9)=25[/tex]
Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]
[tex]x^{2} -9x+7x-63=25[/tex]
Combine like terms:
[tex]x^{2} -2x-63=25[/tex]
Subtract 25 from both sides and obtain:
[tex]x^{2} -2x-88=0[/tex]
Using completing square form:
Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:
[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]
Add 89 to both sides we have:
[tex](x-1)^{2} =89[/tex]
Taking square roots on both sides, obtain:
[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]
Add 1 to both sides we have:
[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]
Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
Know more about square roots here:
https://brainly.com/question/428672
#SPJ4
The complete question is given below:
Use completing the square to solve (x + 7)(x – 9) = 25 for x.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
