x-5x^2-8x+10=0 eching

$$x - 5 x ^ { 2 } - 8 x + 10 = 0$$

x uchun yechish

$$x=\frac{\sqrt{249}-7}{10}\approx 0,877973384$$

$$x=\frac{-\sqrt{249}-7}{10}\approx -2,277973384$$

Kvadrat tenglamalaridan foydalanish qoidalari

-7x ni olish uchun x va -8x ni birlashtirish.

$$-7x-5x^{2}+10=0$$

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.

$$-5x^{2}-7x+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, -7 ni b va 10 ni c bilan almashtiring.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-5\right)\times 10}}{2\left(-5\right)}$$

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-5\right)\times 10}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+20\times 10}}{2\left(-5\right)}$$

20 ni 10 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+200}}{2\left(-5\right)}$$

49 ni 200 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{249}}{2\left(-5\right)}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{249}}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$x=\frac{7±\sqrt{249}}{-10}$$

x=\frac{7±\sqrt{249}}{-10} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{249} ga qo'shish.

$$x=\frac{\sqrt{249}+7}{-10}$$

7+\sqrt{249} ni -10 ga bo'lish.

$$x=\frac{-\sqrt{249}-7}{10}$$

x=\frac{7±\sqrt{249}}{-10} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{249} ni ayirish.

$$x=\frac{7-\sqrt{249}}{-10}$$

7-\sqrt{249} ni -10 ga bo'lish.

$$x=\frac{\sqrt{249}-7}{10}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{249}-7}{10} x=\frac{\sqrt{249}-7}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

-7x ni olish uchun x va -8x ni birlashtirish.

$$-7x-5x^{2}+10=0$$

Ikkala tarafdan 10 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-7x-5x^{2}=-10$$

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

$$-5x^{2}-7x=-10$$

Ikki tarafini -5 ga bo‘ling.

$$\frac{-5x^{2}-7x}{-5}=-\frac{10}{-5}$$

-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{7}{-5}\right)x=-\frac{10}{-5}$$

-7 ni -5 ga bo'lish.

$$x^{2}+\frac{7}{5}x=-\frac{10}{-5}$$

-10 ni -5 ga bo'lish.

$$x^{2}+\frac{7}{5}x=2$$

\frac{7}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{10} olish uchun. Keyin, \frac{7}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{7}{5}x+\left(\frac{7}{10}\right)^{2}=2+\left(\frac{7}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{10} kvadratini chiqarish.

$$x^{2}+\frac{7}{5}x+\frac{49}{100}=2+\frac{49}{100}$$

2 ni \frac{49}{100} ga qo'shish.

$$x^{2}+\frac{7}{5}x+\frac{49}{100}=\frac{249}{100}$$

x^{2}+\frac{7}{5}x+\frac{49}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{7}{10}\right)^{2}=\frac{249}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{10}\right)^{2}}=\sqrt{\frac{249}{100}}$$

Qisqartirish.

$$x+\frac{7}{10}=\frac{\sqrt{249}}{10} x+\frac{7}{10}=-\frac{\sqrt{249}}{10}$$

Tenglamaning ikkala tarafidan \frac{7}{10} ni ayirish.

$$x=\frac{\sqrt{249}-7}{10} x=\frac{-\sqrt{249}-7}{10}$$