(6-x*x)+(7*x)=30 eching

$$(6-x \times x)+(7 \times x)=30$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{47}i+7}{2}\approx 3,5-3,4278273i$$

$$x=\frac{7+\sqrt{47}i}{2}\approx 3,5+3,4278273i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$6-x^{2}+7x=30$$

Ikkala tarafdan 30 ni ayirish.

$$6-x^{2}+7x-30=0$$

-24 olish uchun 6 dan 30 ni ayirish.

$$-24-x^{2}+7x=0$$

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.

$$-x^{2}+7x-24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 7 ni b va -24 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-1\right)\left(-24\right)}}{2\left(-1\right)}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-1\right)\left(-24\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+4\left(-24\right)}}{2\left(-1\right)}$$

4 ni -24 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49-96}}{2\left(-1\right)}$$

49 ni -96 ga qo'shish.

$$x=\frac{-7±\sqrt{-47}}{2\left(-1\right)}$$

-47 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±\sqrt{47}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{47}i}{-2}$$

x=\frac{-7±\sqrt{47}i}{-2} tenglamasini yeching, bunda ± musbat. -7 ni i\sqrt{47} ga qo'shish.

$$x=\frac{-7+\sqrt{47}i}{-2}$$

-7+i\sqrt{47} ni -2 ga bo'lish.

$$x=\frac{-\sqrt{47}i+7}{2}$$

x=\frac{-7±\sqrt{47}i}{-2} tenglamasini yeching, bunda ± manfiy. -7 dan i\sqrt{47} ni ayirish.

$$x=\frac{-\sqrt{47}i-7}{-2}$$

-7-i\sqrt{47} ni -2 ga bo'lish.

$$x=\frac{7+\sqrt{47}i}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{47}i+7}{2} x=\frac{7+\sqrt{47}i}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$6-x^{2}+7x=30$$

Ikkala tarafdan 6 ni ayirish.

$$-x^{2}+7x=30-6$$

24 olish uchun 30 dan 6 ni ayirish.

$$-x^{2}+7x=24$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+7x}{-1}=\frac{24}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{-1}x=\frac{24}{-1}$$

7 ni -1 ga bo'lish.

$$x^{2}-7x=\frac{24}{-1}$$

24 ni -1 ga bo'lish.

$$x^{2}-7x=-24$$

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

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-24+\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=-24+\frac{49}{4}$$

-24 ni \frac{49}{4} ga qo'shish.

$$x^{2}-7x+\frac{49}{4}=-\frac{47}{4}$$

x^{2}-7x+\frac{49}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{7}{2}\right)^{2}=-\frac{47}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{-\frac{47}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{\sqrt{47}i}{2} x-\frac{7}{2}=-\frac{\sqrt{47}i}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{7+\sqrt{47}i}{2} x=\frac{-\sqrt{47}i+7}{2}$$