p^2-38p-24=0 eching

$$p ^ { 2 } - 38 p - 24 = 0$$

p uchun yechish

$$p=\sqrt{385}+19\approx 38,62141687$$

$$p=19-\sqrt{385}\approx -0,62141687$$

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.

$$p^{2}-38p-24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -38 ni b va -24 ni c bilan almashtiring.

$$p=\frac{-\left(-38\right)±\sqrt{\left(-38\right)^{2}-4\left(-24\right)}}{2}$$

-38 kvadratini chiqarish.

$$p=\frac{-\left(-38\right)±\sqrt{1444-4\left(-24\right)}}{2}$$

-4 ni -24 marotabaga ko'paytirish.

$$p=\frac{-\left(-38\right)±\sqrt{1444+96}}{2}$$

1444 ni 96 ga qo'shish.

$$p=\frac{-\left(-38\right)±\sqrt{1540}}{2}$$

1540 ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-38\right)±2\sqrt{385}}{2}$$

-38 ning teskarisi 38 ga teng.

$$p=\frac{38±2\sqrt{385}}{2}$$

p=\frac{38±2\sqrt{385}}{2} tenglamasini yeching, bunda ± musbat. 38 ni 2\sqrt{385} ga qo'shish.

$$p=\frac{2\sqrt{385}+38}{2}$$

38+2\sqrt{385} ni 2 ga bo'lish.

$$p=\sqrt{385}+19$$

p=\frac{38±2\sqrt{385}}{2} tenglamasini yeching, bunda ± manfiy. 38 dan 2\sqrt{385} ni ayirish.

$$p=\frac{38-2\sqrt{385}}{2}$$

38-2\sqrt{385} ni 2 ga bo'lish.

$$p=19-\sqrt{385}$$

Tenglama yechildi.

$$p=\sqrt{385}+19 p=19-\sqrt{385}$$

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.

$$p^{2}-38p-24=0$$

24 ni tenglamaning ikkala tarafiga qo'shish.

$$p^{2}-38p-24-\left(-24\right)=-\left(-24\right)$$

O‘zidan -24 ayirilsa 0 qoladi.

$$p^{2}-38p=-\left(-24\right)$$

0 dan -24 ni ayirish.

$$p^{2}-38p=24$$

-38 ni bo‘lish, x shartining koeffitsienti, 2 ga -19 olish uchun. Keyin, -19 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$p^{2}-38p+\left(-19\right)^{2}=24+\left(-19\right)^{2}$$

-19 kvadratini chiqarish.

$$p^{2}-38p+361=24+361$$

24 ni 361 ga qo'shish.

$$p^{2}-38p+361=385$$

p^{2}-38p+361 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(p-19\right)^{2}=385$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-19\right)^{2}}=\sqrt{385}$$

Qisqartirish.

$$p-19=\sqrt{385} p-19=-\sqrt{385}$$

19 ni tenglamaning ikkala tarafiga qo'shish.

$$p=\sqrt{385}+19 p=19-\sqrt{385}$$