15-x^2+4x-5=0 eching

$$15 - x ^ { 2 } + 4 x - 5 = 0$$

x uchun yechish

$$x=\sqrt{14}+2\approx 5,741657387$$

$$x=2-\sqrt{14}\approx -1,741657387$$

Kvadrat tenglamalaridan foydalanish qoidalari

10 olish uchun 15 dan 5 ni ayirish.

$$10-x^{2}+4x=0$$

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.

$$-x^{2}+4x+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 4 ni b va 10 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4\times 10}}{2\left(-1\right)}$$

4 ni 10 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+40}}{2\left(-1\right)}$$

16 ni 40 ga qo'shish.

$$x=\frac{-4±\sqrt{56}}{2\left(-1\right)}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{14}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{14}}{-2}$$

x=\frac{-4±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}-4}{-2}$$

-4+2\sqrt{14} ni -2 ga bo'lish.

$$x=2-\sqrt{14}$$

x=\frac{-4±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{14} ni ayirish.

$$x=\frac{-2\sqrt{14}-4}{-2}$$

-4-2\sqrt{14} ni -2 ga bo'lish.

$$x=\sqrt{14}+2$$

Tenglama yechildi.

$$x=2-\sqrt{14} x=\sqrt{14}+2$$

Kvadratni yakunlash bo'yicha qadamlar

10 olish uchun 15 dan 5 ni ayirish.

$$10-x^{2}+4x=0$$

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

$$-x^{2}+4x=-10$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+4x}{-1}=-\frac{10}{-1}$$

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

$$x^{2}+\frac{4}{-1}x=-\frac{10}{-1}$$

4 ni -1 ga bo'lish.

$$x^{2}-4x=-\frac{10}{-1}$$

-10 ni -1 ga bo'lish.

$$x^{2}-4x=10$$

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

$$x^{2}-4x+\left(-2\right)^{2}=10+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=10+4$$

10 ni 4 ga qo'shish.

$$x^{2}-4x+4=14$$

x^{2}-4x+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.

$$\left(x-2\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x-2=\sqrt{14} x-2=-\sqrt{14}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{14}+2 x=2-\sqrt{14}$$