(a)=9a^2+46a.text{solvefor}h(a)=-5 eching

$$( a ) = 9 a ^ { 2 } + 46 a . \text { solve for } h ( a ) = - 5$$

a uchun yechish

$$a=-5$$

$$a=0$$

Faktorlash qadamlari

Ikkala tarafdan 9a^{2} ni ayirish.

$$a-9a^{2}=46a$$

Ikkala tarafdan 46a ni ayirish.

$$a-9a^{2}-46a=0$$

-45a ni olish uchun a va -46a ni birlashtirish.

$$-45a-9a^{2}=0$$

a omili.

$$a\left(-45-9a\right)=0$$

Tenglamani yechish uchun a=0 va -45-9a=0 ni yeching.

$$a=0 a=-5$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 9a^{2} ni ayirish.

$$a-9a^{2}=46a$$

Ikkala tarafdan 46a ni ayirish.

$$a-9a^{2}-46a=0$$

-45a ni olish uchun a va -46a ni birlashtirish.

$$-45a-9a^{2}=0$$

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.

$$-9a^{2}-45a=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -9 ni a, -45 ni b va 0 ni c bilan almashtiring.

$$a=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}}}{2\left(-9\right)}$$

\left(-45\right)^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-45\right)±45}{2\left(-9\right)}$$

-45 ning teskarisi 45 ga teng.

$$a=\frac{45±45}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$a=\frac{45±45}{-18}$$

a=\frac{45±45}{-18} tenglamasini yeching, bunda ± musbat. 45 ni 45 ga qo'shish.

$$a=\frac{90}{-18}$$

90 ni -18 ga bo'lish.

$$a=-5$$

a=\frac{45±45}{-18} tenglamasini yeching, bunda ± manfiy. 45 dan 45 ni ayirish.

$$a=\frac{0}{-18}$$

0 ni -18 ga bo'lish.

$$a=0$$

Tenglama yechildi.

$$a=-5 a=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 9a^{2} ni ayirish.

$$a-9a^{2}=46a$$

Ikkala tarafdan 46a ni ayirish.

$$a-9a^{2}-46a=0$$

-45a ni olish uchun a va -46a ni birlashtirish.

$$-45a-9a^{2}=0$$

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

$$-9a^{2}-45a=0$$

Ikki tarafini -9 ga bo‘ling.

$$\frac{-9a^{2}-45a}{-9}=\frac{0}{-9}$$

-9 ga bo'lish -9 ga ko'paytirishni bekor qiladi.

$$a^{2}+\left(-\frac{45}{-9}\right)a=\frac{0}{-9}$$

-45 ni -9 ga bo'lish.

$$a^{2}+5a=\frac{0}{-9}$$

0 ni -9 ga bo'lish.

$$a^{2}+5a=0$$

5 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{2} olish uchun. Keyin, \frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}+5a+\left(\frac{5}{2}\right)^{2}=\left(\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{2} kvadratini chiqarish.

$$a^{2}+5a+\frac{25}{4}=\frac{25}{4}$$

a^{2}+5a+\frac{25}{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.

$$\left(a+\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$a+\frac{5}{2}=\frac{5}{2} a+\frac{5}{2}=-\frac{5}{2}$$

Tenglamaning ikkala tarafidan \frac{5}{2} ni ayirish.

$$a=0 a=-5$$