Maligayang pagdating sa Imhr.ca, kung saan maaari kang makakuha ng mga sagot mula sa mga eksperto nang mabilis at tumpak. Kumuha ng mabilis at mapagkakatiwalaang solusyon sa iyong mga tanong mula sa isang komunidad ng mga bihasang eksperto. Tuklasin ang komprehensibong mga solusyon sa iyong mga tanong mula sa mga bihasang propesyonal sa iba't ibang larangan sa aming platform.
Sagot :
a. Factoring - since the it can be factored to (3x - 5)(3x + 5) by Binomial Theorem.
b. Factoring - binomial theorem is also applied (2x - 11)(2x + 11)
c. Quadratic Equation - can not be factored easily
d. Factoring - can be factored (2x - 7)(x + 4)
e. Factoring - can be factored (2x + 3)(2x + 5)
f. Factoring - can be factored (2x - 3)(2x + 5)
[tex]a.\\ 9x^2 = 225 \\9x^2-225=0\\(3x)^2-15^2=0\\(3x-15)(3x+15)=0 \\3x-15=0\ \ or\ \ 3x+15 =0 \\3x=15 \ \ or \ \ 3x=-15 \\x= 3 \ \ or\ \ x=-3\\ \\Factoring : \ a^2-b^2=(a-b)(a+b)[/tex]
[tex]b.\\\\ 4x^2 - 121 = 0\\(2x)^2-11^2 =0\\(2x-11)(2x+11)=0 \\\\2x-11=0 \ \ or \ \ 2x+11=0 \\2x=11 \ \ or \ \ 2x=-11\\ x=\frac{11}{2} \ \ or \ \ x=-\frac{11}{2} \\ x=5.5 \ \ or \ \ x=-5.5 \\Factoring[/tex]
[tex]c.\\\\ x^2 + 11x + 30 = 0 \\a=1, \ \ b=11, \ \c=30 \\\\ \Delta =b^2-4ac = 11^2 -4\cdot1\cdot 30 = 121-120=1 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-11-\sqrt{1 }}{2 }=\frac{ -11-1}{2}=\frac{-12}{2}=-6 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-11+\sqrt{1 }}{2 }=\frac{ -11+1}{2}=\frac{-10}{2}=-5\\\\ Quadratic \ Equation - can \ not \ be \ easily \ decomposed \ into \ factors[/tex]
[tex]d.\\\\ 2x^2 + x - 28 = 0 \\a=2, \ \ b=1 , \ \c=-28 \\\\ \Delta =b^2-4ac = 1^2 -4\cdot2\cdot (-28) = 1+224=225 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-1-\sqrt{225}}{2\cdot 2 }=\frac{ -1-15}{4}=\frac{-16}{4}=-4 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-1+\sqrt{225}}{2\cdot 2 }=\frac{ -1+15}{4}=\frac{ 14}{4}= 3.5\\\\ Quadratic \ Equation[/tex]
[tex]e. \\\\4x^2 + 16x + 15 = 0 \\a=4, \ \ b=16 , \ \c=15 \\\\ \Delta =b^2-4ac = 16^2 -4\cdot4\cdot 15 = 256-240=16 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-16-\sqrt{16}}{2\cdot 4 }=\frac{ -16-4}{8}=\frac{-20}{8}=- \frac{5}{2}=-2.5 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-16+\sqrt{16}}{2\cdot 4 }=\frac{ -16+4}{8}=\frac{-12}{8}=- \frac{3}{2}=-1.5\\\\ Quadratic \ Equation[/tex]
[tex]e.\\\\ 4x^2 + 4x - 15 = 0 \\a=4, \ \ b=4, \ \c=-15 \\\\ \Delta =b^2-4ac = 4^2 -4\cdot4\cdot (- 15 )= 16+240=256 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-4-\sqrt{256}}{2\cdot 4 }=\frac{ -4-16 }{8}=\frac{-20}{8}=- \frac{5}{2}=-2.5 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-4+\sqrt{256}}{2\cdot 4 }=\frac{ -4+16}{8}=\frac{ 12}{8}= \frac{3}{2}= 1.5\\\\ Quadratic \ Equation[/tex]
[tex]b.\\\\ 4x^2 - 121 = 0\\(2x)^2-11^2 =0\\(2x-11)(2x+11)=0 \\\\2x-11=0 \ \ or \ \ 2x+11=0 \\2x=11 \ \ or \ \ 2x=-11\\ x=\frac{11}{2} \ \ or \ \ x=-\frac{11}{2} \\ x=5.5 \ \ or \ \ x=-5.5 \\Factoring[/tex]
[tex]c.\\\\ x^2 + 11x + 30 = 0 \\a=1, \ \ b=11, \ \c=30 \\\\ \Delta =b^2-4ac = 11^2 -4\cdot1\cdot 30 = 121-120=1 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-11-\sqrt{1 }}{2 }=\frac{ -11-1}{2}=\frac{-12}{2}=-6 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-11+\sqrt{1 }}{2 }=\frac{ -11+1}{2}=\frac{-10}{2}=-5\\\\ Quadratic \ Equation - can \ not \ be \ easily \ decomposed \ into \ factors[/tex]
[tex]d.\\\\ 2x^2 + x - 28 = 0 \\a=2, \ \ b=1 , \ \c=-28 \\\\ \Delta =b^2-4ac = 1^2 -4\cdot2\cdot (-28) = 1+224=225 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-1-\sqrt{225}}{2\cdot 2 }=\frac{ -1-15}{4}=\frac{-16}{4}=-4 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-1+\sqrt{225}}{2\cdot 2 }=\frac{ -1+15}{4}=\frac{ 14}{4}= 3.5\\\\ Quadratic \ Equation[/tex]
[tex]e. \\\\4x^2 + 16x + 15 = 0 \\a=4, \ \ b=16 , \ \c=15 \\\\ \Delta =b^2-4ac = 16^2 -4\cdot4\cdot 15 = 256-240=16 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-16-\sqrt{16}}{2\cdot 4 }=\frac{ -16-4}{8}=\frac{-20}{8}=- \frac{5}{2}=-2.5 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-16+\sqrt{16}}{2\cdot 4 }=\frac{ -16+4}{8}=\frac{-12}{8}=- \frac{3}{2}=-1.5\\\\ Quadratic \ Equation[/tex]
[tex]e.\\\\ 4x^2 + 4x - 15 = 0 \\a=4, \ \ b=4, \ \c=-15 \\\\ \Delta =b^2-4ac = 4^2 -4\cdot4\cdot (- 15 )= 16+240=256 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-4-\sqrt{256}}{2\cdot 4 }=\frac{ -4-16 }{8}=\frac{-20}{8}=- \frac{5}{2}=-2.5 \\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-4+\sqrt{256}}{2\cdot 4 }=\frac{ -4+16}{8}=\frac{ 12}{8}= \frac{3}{2}= 1.5\\\\ Quadratic \ Equation[/tex]
Umaasa kaming naging kapaki-pakinabang ang aming mga sagot. Bumalik anumang oras para sa higit pang tumpak na mga sagot at napapanahong impormasyon. Salamat sa pagpunta. Nagsusumikap kaming magbigay ng pinakamahusay na mga sagot para sa lahat ng iyong mga katanungan. Kita tayo muli sa susunod. Maraming salamat sa paggamit ng Imhr.ca. Balik-balikan kami para sa mga kasagutan sa inyong mga tanong.