2x^2-28x+171=0 eching

$$2 x ^ { 2 } - 28 x + 171 = 0$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{146}i}{2}+7\approx 7+6,041522987i$$

$$x=-\frac{\sqrt{146}i}{2}+7\approx 7-6,041522987i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$2x^{2}-28x+171=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -28 ni b va 171 ni c bilan almashtiring.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}-4\times 2\times 171}}{2\times 2}$$

-28 kvadratini chiqarish.

$$x=\frac{-\left(-28\right)±\sqrt{784-4\times 2\times 171}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-28\right)±\sqrt{784-8\times 171}}{2\times 2}$$

-8 ni 171 marotabaga ko'paytirish.

$$x=\frac{-\left(-28\right)±\sqrt{784-1368}}{2\times 2}$$

784 ni -1368 ga qo'shish.

$$x=\frac{-\left(-28\right)±\sqrt{-584}}{2\times 2}$$

-584 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28\right)±2\sqrt{146}i}{2\times 2}$$

-28 ning teskarisi 28 ga teng.

$$x=\frac{28±2\sqrt{146}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{28±2\sqrt{146}i}{4}$$

x=\frac{28±2\sqrt{146}i}{4} tenglamasini yeching, bunda ± musbat. 28 ni 2i\sqrt{146} ga qo'shish.

$$x=\frac{28+2\sqrt{146}i}{4}$$

28+2i\sqrt{146} ni 4 ga bo'lish.

$$x=\frac{\sqrt{146}i}{2}+7$$

x=\frac{28±2\sqrt{146}i}{4} tenglamasini yeching, bunda ± manfiy. 28 dan 2i\sqrt{146} ni ayirish.

$$x=\frac{-2\sqrt{146}i+28}{4}$$

28-2i\sqrt{146} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{146}i}{2}+7$$

Tenglama yechildi.

$$x=\frac{\sqrt{146}i}{2}+7 x=-\frac{\sqrt{146}i}{2}+7$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$2x^{2}-28x+171=0$$

Tenglamaning ikkala tarafidan 171 ni ayirish.

$$2x^{2}-28x+171-171=-171$$

O‘zidan 171 ayirilsa 0 qoladi.

$$2x^{2}-28x=-171$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-28x}{2}=-\frac{171}{2}$$

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

$$x^{2}+\left(-\frac{28}{2}\right)x=-\frac{171}{2}$$

-28 ni 2 ga bo'lish.

$$x^{2}-14x=-\frac{171}{2}$$

-14 ni bo‘lish, x shartining koeffitsienti, 2 ga -7 olish uchun. Keyin, -7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-14x+\left(-7\right)^{2}=-\frac{171}{2}+\left(-7\right)^{2}$$

-7 kvadratini chiqarish.

$$x^{2}-14x+49=-\frac{171}{2}+49$$

-\frac{171}{2} ni 49 ga qo'shish.

$$x^{2}-14x+49=-\frac{73}{2}$$

x^{2}-14x+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-7\right)^{2}=-\frac{73}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{-\frac{73}{2}}$$

Qisqartirish.

$$x-7=\frac{\sqrt{146}i}{2} x-7=-\frac{\sqrt{146}i}{2}$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{146}i}{2}+7 x=-\frac{\sqrt{146}i}{2}+7$$