(2)-x^2+8x+9=0 eching

$$( 2 ) - x ^ { 2 } + 8 x + 9 = 0$$

x uchun yechish

$$x=3\sqrt{3}+4\approx 9,196152423$$

$$x=4-3\sqrt{3}\approx -1,196152423$$

Kvadrat tenglamalaridan foydalanish qoidalari

11 olish uchun 2 va 9'ni qo'shing.

$$11-x^{2}+8x=0$$

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.

$$-x^{2}+8x+11=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 8 ni b va 11 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+4\times 11}}{2\left(-1\right)}$$

4 ni 11 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+44}}{2\left(-1\right)}$$

64 ni 44 ga qo'shish.

$$x=\frac{-8±\sqrt{108}}{2\left(-1\right)}$$

108 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±6\sqrt{3}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-8±6\sqrt{3}}{-2}$$

x=\frac{-8±6\sqrt{3}}{-2} tenglamasini yeching, bunda ± musbat. -8 ni 6\sqrt{3} ga qo'shish.

$$x=\frac{6\sqrt{3}-8}{-2}$$

-8+6\sqrt{3} ni -2 ga bo'lish.

$$x=4-3\sqrt{3}$$

x=\frac{-8±6\sqrt{3}}{-2} tenglamasini yeching, bunda ± manfiy. -8 dan 6\sqrt{3} ni ayirish.

$$x=\frac{-6\sqrt{3}-8}{-2}$$

-8-6\sqrt{3} ni -2 ga bo'lish.

$$x=3\sqrt{3}+4$$

Tenglama yechildi.

$$x=4-3\sqrt{3} x=3\sqrt{3}+4$$

Kvadratni yakunlash bo'yicha qadamlar

11 olish uchun 2 va 9'ni qo'shing.

$$11-x^{2}+8x=0$$

Ikkala tarafdan 11 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x^{2}+8x=-11$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+8x}{-1}=-\frac{11}{-1}$$

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

$$x^{2}+\frac{8}{-1}x=-\frac{11}{-1}$$

8 ni -1 ga bo'lish.

$$x^{2}-8x=-\frac{11}{-1}$$

-11 ni -1 ga bo'lish.

$$x^{2}-8x=11$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=11+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=11+16$$

11 ni 16 ga qo'shish.

$$x^{2}-8x+16=27$$

x^{2}-8x+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.

$$\left(x-4\right)^{2}=27$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{27}$$

Qisqartirish.

$$x-4=3\sqrt{3} x-4=-3\sqrt{3}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=3\sqrt{3}+4 x=4-3\sqrt{3}$$