(x)=3x^2+6x-24 eching

$$( x ) = 3 x ^ { 2 } + 6 x - 24$$

x uchun yechish

$$x = \frac{\sqrt{313} - 5}{6} \approx 2,115301002$$

$$x=\frac{-\sqrt{313}-5}{6}\approx -3,781967669$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3x^{2} ni ayirish.

$$x-3x^{2}=6x-24$$

Ikkala tarafdan 6x ni ayirish.

$$x-3x^{2}-6x=-24$$

-5x ni olish uchun x va -6x ni birlashtirish.

$$-5x-3x^{2}=-24$$

24 ni ikki tarafga qo’shing.

$$-5x-3x^{2}+24=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-3x^{2}-5x+24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, -5 ni b va 24 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-3\right)\times 24}}{2\left(-3\right)}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-3\right)\times 24}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+12\times 24}}{2\left(-3\right)}$$

12 ni 24 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+288}}{2\left(-3\right)}$$

25 ni 288 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{313}}{2\left(-3\right)}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±\sqrt{313}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{5±\sqrt{313}}{-6}$$

x=\frac{5±\sqrt{313}}{-6} tenglamasini yeching, bunda ± musbat. 5 ni \sqrt{313} ga qo'shish.

$$x=\frac{\sqrt{313}+5}{-6}$$

5+\sqrt{313} ni -6 ga bo'lish.

$$x=\frac{-\sqrt{313}-5}{6}$$

x=\frac{5±\sqrt{313}}{-6} tenglamasini yeching, bunda ± manfiy. 5 dan \sqrt{313} ni ayirish.

$$x=\frac{5-\sqrt{313}}{-6}$$

5-\sqrt{313} ni -6 ga bo'lish.

$$x=\frac{\sqrt{313}-5}{6}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{313}-5}{6} x=\frac{\sqrt{313}-5}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 3x^{2} ni ayirish.

$$x-3x^{2}=6x-24$$

Ikkala tarafdan 6x ni ayirish.

$$x-3x^{2}-6x=-24$$

-5x ni olish uchun x va -6x ni birlashtirish.

$$-5x-3x^{2}=-24$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-3x^{2}-5x=-24$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}-5x}{-3}=-\frac{24}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{5}{-3}\right)x=-\frac{24}{-3}$$

-5 ni -3 ga bo'lish.

$$x^{2}+\frac{5}{3}x=-\frac{24}{-3}$$

-24 ni -3 ga bo'lish.

$$x^{2}+\frac{5}{3}x=8$$

\frac{5}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{6} olish uchun. Keyin, \frac{5}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{5}{3}x+\left(\frac{5}{6}\right)^{2}=8+\left(\frac{5}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{6} kvadratini chiqarish.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=8+\frac{25}{36}$$

8 ni \frac{25}{36} ga qo'shish.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{313}{36}$$

x^{2}+\frac{5}{3}x+\frac{25}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{5}{6}\right)^{2}=\frac{313}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{6}\right)^{2}}=\sqrt{\frac{313}{36}}$$

Qisqartirish.

$$x+\frac{5}{6}=\frac{\sqrt{313}}{6} x+\frac{5}{6}=-\frac{\sqrt{313}}{6}$$

Tenglamaning ikkala tarafidan \frac{5}{6} ni ayirish.

$$x=\frac{\sqrt{313}-5}{6} x=\frac{-\sqrt{313}-5}{6}$$