-4(x)=2x^2+7x-4 eching

$$-4(x)=2 { x }^{ 2 } +7x-4$$

x uchun yechish

$$x=\frac{3\sqrt{17}-11}{4}\approx 0,342329219$$

$$x=\frac{-3\sqrt{17}-11}{4}\approx -5,842329219$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x^{2} ni ayirish.

$$-4x-2x^{2}=7x-4$$

Ikkala tarafdan 7x ni ayirish.

$$-4x-2x^{2}-7x=-4$$

-11x ni olish uchun -4x va -7x ni birlashtirish.

$$-11x-2x^{2}=-4$$

4 ni ikki tarafga qo’shing.

$$-11x-2x^{2}+4=0$$

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.

$$-2x^{2}-11x+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -11 ni b va 4 ni c bilan almashtiring.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

-11 kvadratini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121+8\times 4}}{2\left(-2\right)}$$

8 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121+32}}{2\left(-2\right)}$$

121 ni 32 ga qo'shish.

$$x=\frac{-\left(-11\right)±\sqrt{153}}{2\left(-2\right)}$$

153 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±3\sqrt{17}}{2\left(-2\right)}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±3\sqrt{17}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{11±3\sqrt{17}}{-4}$$

x=\frac{11±3\sqrt{17}}{-4} tenglamasini yeching, bunda ± musbat. 11 ni 3\sqrt{17} ga qo'shish.

$$x=\frac{3\sqrt{17}+11}{-4}$$

11+3\sqrt{17} ni -4 ga bo'lish.

$$x=\frac{-3\sqrt{17}-11}{4}$$

x=\frac{11±3\sqrt{17}}{-4} tenglamasini yeching, bunda ± manfiy. 11 dan 3\sqrt{17} ni ayirish.

$$x=\frac{11-3\sqrt{17}}{-4}$$

11-3\sqrt{17} ni -4 ga bo'lish.

$$x=\frac{3\sqrt{17}-11}{4}$$

Tenglama yechildi.

$$x=\frac{-3\sqrt{17}-11}{4} x=\frac{3\sqrt{17}-11}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x^{2} ni ayirish.

$$-4x-2x^{2}=7x-4$$

Ikkala tarafdan 7x ni ayirish.

$$-4x-2x^{2}-7x=-4$$

-11x ni olish uchun -4x va -7x ni birlashtirish.

$$-11x-2x^{2}=-4$$

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

$$-2x^{2}-11x=-4$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-11x}{-2}=-\frac{4}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{11}{-2}\right)x=-\frac{4}{-2}$$

-11 ni -2 ga bo'lish.

$$x^{2}+\frac{11}{2}x=-\frac{4}{-2}$$

-4 ni -2 ga bo'lish.

$$x^{2}+\frac{11}{2}x=2$$

\frac{11}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{11}{4} olish uchun. Keyin, \frac{11}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{11}{2}x+\left(\frac{11}{4}\right)^{2}=2+\left(\frac{11}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{11}{4} kvadratini chiqarish.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=2+\frac{121}{16}$$

2 ni \frac{121}{16} ga qo'shish.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=\frac{153}{16}$$

x^{2}+\frac{11}{2}x+\frac{121}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{11}{4}\right)^{2}=\frac{153}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{11}{4}\right)^{2}}=\sqrt{\frac{153}{16}}$$

Qisqartirish.

$$x+\frac{11}{4}=\frac{3\sqrt{17}}{4} x+\frac{11}{4}=-\frac{3\sqrt{17}}{4}$$

Tenglamaning ikkala tarafidan \frac{11}{4} ni ayirish.

$$x=\frac{3\sqrt{17}-11}{4} x=\frac{-3\sqrt{17}-11}{4}$$