a^2+8a+9=96 eching

$$a ^ { 2 } + 8 a + 9 = 96$$

a uchun yechish (complex solution)

$$a=\sqrt{103}-4\approx 6,148891565$$

$$a=-\left(\sqrt{103}+4\right)\approx -14,148891565$$

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.

$$a^{2}+8a+9=96$$

Tenglamaning ikkala tarafidan 96 ni ayirish.

$$a^{2}+8a+9-96=96-96$$

O‘zidan 96 ayirilsa 0 qoladi.

$$a^{2}+8a+9-96=0$$

9 dan 96 ni ayirish.

$$a^{2}+8a-87=0$$

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 -87 ni c bilan almashtiring.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-87\right)}}{2}$$

8 kvadratini chiqarish.

$$a=\frac{-8±\sqrt{64-4\left(-87\right)}}{2}$$

-4 ni -87 marotabaga ko'paytirish.

$$a=\frac{-8±\sqrt{64+348}}{2}$$

64 ni 348 ga qo'shish.

$$a=\frac{-8±\sqrt{412}}{2}$$

412 ning kvadrat ildizini chiqarish.

$$a=\frac{-8±2\sqrt{103}}{2}$$

a=\frac{-8±2\sqrt{103}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{103} ga qo'shish.

$$a=\frac{2\sqrt{103}-8}{2}$$

-8+2\sqrt{103} ni 2 ga bo'lish.

$$a=\sqrt{103}-4$$

a=\frac{-8±2\sqrt{103}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{103} ni ayirish.

$$a=\frac{-2\sqrt{103}-8}{2}$$

-8-2\sqrt{103} ni 2 ga bo'lish.

$$a=-\sqrt{103}-4$$

Tenglama yechildi.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

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.

$$a^{2}+8a+9=96$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$a^{2}+8a+9-9=96-9$$

O‘zidan 9 ayirilsa 0 qoladi.

$$a^{2}+8a=96-9$$

96 dan 9 ni ayirish.

$$a^{2}+8a=87$$

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.

$$a^{2}+8a+4^{2}=87+4^{2}$$

4 kvadratini chiqarish.

$$a^{2}+8a+16=87+16$$

87 ni 16 ga qo'shish.

$$a^{2}+8a+16=103$$

a^{2}+8a+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.

$$\left(a+4\right)^{2}=103$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+4\right)^{2}}=\sqrt{103}$$

Qisqartirish.

$$a+4=\sqrt{103} a+4=-\sqrt{103}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

a uchun yechish

$$a=\sqrt{103}-4\approx 6,148891565$$

$$a=-\sqrt{103}-4\approx -14,148891565$$

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.

$$a^{2}+8a+9=96$$

Tenglamaning ikkala tarafidan 96 ni ayirish.

$$a^{2}+8a+9-96=96-96$$

O‘zidan 96 ayirilsa 0 qoladi.

$$a^{2}+8a+9-96=0$$

9 dan 96 ni ayirish.

$$a^{2}+8a-87=0$$

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 -87 ni c bilan almashtiring.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-87\right)}}{2}$$

8 kvadratini chiqarish.

$$a=\frac{-8±\sqrt{64-4\left(-87\right)}}{2}$$

-4 ni -87 marotabaga ko'paytirish.

$$a=\frac{-8±\sqrt{64+348}}{2}$$

64 ni 348 ga qo'shish.

$$a=\frac{-8±\sqrt{412}}{2}$$

412 ning kvadrat ildizini chiqarish.

$$a=\frac{-8±2\sqrt{103}}{2}$$

a=\frac{-8±2\sqrt{103}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{103} ga qo'shish.

$$a=\frac{2\sqrt{103}-8}{2}$$

-8+2\sqrt{103} ni 2 ga bo'lish.

$$a=\sqrt{103}-4$$

a=\frac{-8±2\sqrt{103}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{103} ni ayirish.

$$a=\frac{-2\sqrt{103}-8}{2}$$

-8-2\sqrt{103} ni 2 ga bo'lish.

$$a=-\sqrt{103}-4$$

Tenglama yechildi.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$

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.

$$a^{2}+8a+9=96$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$a^{2}+8a+9-9=96-9$$

O‘zidan 9 ayirilsa 0 qoladi.

$$a^{2}+8a=96-9$$

96 dan 9 ni ayirish.

$$a^{2}+8a=87$$

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.

$$a^{2}+8a+4^{2}=87+4^{2}$$

4 kvadratini chiqarish.

$$a^{2}+8a+16=87+16$$

87 ni 16 ga qo'shish.

$$a^{2}+8a+16=103$$

a^{2}+8a+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.

$$\left(a+4\right)^{2}=103$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+4\right)^{2}}=\sqrt{103}$$

Qisqartirish.

$$a+4=\sqrt{103} a+4=-\sqrt{103}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$a=\sqrt{103}-4 a=-\sqrt{103}-4$$