q^2+6q-18=-5 eching

$$q ^ { 2 } + 6 q - 18 = - 5$$

q uchun yechish (complex solution)

$$q=\sqrt{22}-3\approx 1,69041576$$

$$q=-\left(\sqrt{22}+3\right)\approx -7,69041576$$

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.

$$q^{2}+6q-18=-5$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$q^{2}+6q-18-\left(-5\right)=-5-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$q^{2}+6q-18-\left(-5\right)=0$$

-18 dan -5 ni ayirish.

$$q^{2}+6q-13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va -13 ni c bilan almashtiring.

$$q=\frac{-6±\sqrt{6^{2}-4\left(-13\right)}}{2}$$

6 kvadratini chiqarish.

$$q=\frac{-6±\sqrt{36-4\left(-13\right)}}{2}$$

-4 ni -13 marotabaga ko'paytirish.

$$q=\frac{-6±\sqrt{36+52}}{2}$$

36 ni 52 ga qo'shish.

$$q=\frac{-6±\sqrt{88}}{2}$$

88 ning kvadrat ildizini chiqarish.

$$q=\frac{-6±2\sqrt{22}}{2}$$

q=\frac{-6±2\sqrt{22}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{22} ga qo'shish.

$$q=\frac{2\sqrt{22}-6}{2}$$

-6+2\sqrt{22} ni 2 ga bo'lish.

$$q=\sqrt{22}-3$$

q=\frac{-6±2\sqrt{22}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{22} ni ayirish.

$$q=\frac{-2\sqrt{22}-6}{2}$$

-6-2\sqrt{22} ni 2 ga bo'lish.

$$q=-\sqrt{22}-3$$

Tenglama yechildi.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

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.

$$q^{2}+6q-18=-5$$

18 ni tenglamaning ikkala tarafiga qo'shish.

$$q^{2}+6q-18-\left(-18\right)=-5-\left(-18\right)$$

O‘zidan -18 ayirilsa 0 qoladi.

$$q^{2}+6q=-5-\left(-18\right)$$

-5 dan -18 ni ayirish.

$$q^{2}+6q=13$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$q^{2}+6q+3^{2}=13+3^{2}$$

3 kvadratini chiqarish.

$$q^{2}+6q+9=13+9$$

13 ni 9 ga qo'shish.

$$q^{2}+6q+9=22$$

q^{2}+6q+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(q+3\right)^{2}=22$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(q+3\right)^{2}}=\sqrt{22}$$

Qisqartirish.

$$q+3=\sqrt{22} q+3=-\sqrt{22}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

q uchun yechish

$$q=\sqrt{22}-3\approx 1,69041576$$

$$q=-\sqrt{22}-3\approx -7,69041576$$

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.

$$q^{2}+6q-18=-5$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$q^{2}+6q-18-\left(-5\right)=-5-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$q^{2}+6q-18-\left(-5\right)=0$$

-18 dan -5 ni ayirish.

$$q^{2}+6q-13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va -13 ni c bilan almashtiring.

$$q=\frac{-6±\sqrt{6^{2}-4\left(-13\right)}}{2}$$

6 kvadratini chiqarish.

$$q=\frac{-6±\sqrt{36-4\left(-13\right)}}{2}$$

-4 ni -13 marotabaga ko'paytirish.

$$q=\frac{-6±\sqrt{36+52}}{2}$$

36 ni 52 ga qo'shish.

$$q=\frac{-6±\sqrt{88}}{2}$$

88 ning kvadrat ildizini chiqarish.

$$q=\frac{-6±2\sqrt{22}}{2}$$

q=\frac{-6±2\sqrt{22}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{22} ga qo'shish.

$$q=\frac{2\sqrt{22}-6}{2}$$

-6+2\sqrt{22} ni 2 ga bo'lish.

$$q=\sqrt{22}-3$$

q=\frac{-6±2\sqrt{22}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{22} ni ayirish.

$$q=\frac{-2\sqrt{22}-6}{2}$$

-6-2\sqrt{22} ni 2 ga bo'lish.

$$q=-\sqrt{22}-3$$

Tenglama yechildi.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

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.

$$q^{2}+6q-18=-5$$

18 ni tenglamaning ikkala tarafiga qo'shish.

$$q^{2}+6q-18-\left(-18\right)=-5-\left(-18\right)$$

O‘zidan -18 ayirilsa 0 qoladi.

$$q^{2}+6q=-5-\left(-18\right)$$

-5 dan -18 ni ayirish.

$$q^{2}+6q=13$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$q^{2}+6q+3^{2}=13+3^{2}$$

3 kvadratini chiqarish.

$$q^{2}+6q+9=13+9$$

13 ni 9 ga qo'shish.

$$q^{2}+6q+9=22$$

q^{2}+6q+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(q+3\right)^{2}=22$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(q+3\right)^{2}}=\sqrt{22}$$

Qisqartirish.

$$q+3=\sqrt{22} q+3=-\sqrt{22}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$