0=a^2+5a-40 eching

$$0 = a ^ { 2 } + 5 a - 40$$

a uchun yechish

$$a = \frac{\sqrt{185} - 5}{2} \approx 4,300735254$$

$$a=\frac{-\sqrt{185}-5}{2}\approx -9,300735254$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$a^{2}+5a-40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 5 ni b va -40 ni c bilan almashtiring.

$$a=\frac{-5±\sqrt{5^{2}-4\left(-40\right)}}{2}$$

5 kvadratini chiqarish.

$$a=\frac{-5±\sqrt{25-4\left(-40\right)}}{2}$$

-4 ni -40 marotabaga ko'paytirish.

$$a=\frac{-5±\sqrt{25+160}}{2}$$

25 ni 160 ga qo'shish.

$$a=\frac{-5±\sqrt{185}}{2}$$

a=\frac{-5±\sqrt{185}}{2} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{185} ga qo'shish.

$$a=\frac{\sqrt{185}-5}{2}$$

a=\frac{-5±\sqrt{185}}{2} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{185} ni ayirish.

$$a=\frac{-\sqrt{185}-5}{2}$$

Tenglama yechildi.

$$a=\frac{\sqrt{185}-5}{2} a=\frac{-\sqrt{185}-5}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$a^{2}+5a-40=0$$

40 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$a^{2}+5a=40$$

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.

$$a^{2}+5a+\left(\frac{5}{2}\right)^{2}=40+\left(\frac{5}{2}\right)^{2}$$

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

$$a^{2}+5a+\frac{25}{4}=40+\frac{25}{4}$$

40 ni \frac{25}{4} ga qo'shish.

$$a^{2}+5a+\frac{25}{4}=\frac{185}{4}$$

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.

$$\left(a+\frac{5}{2}\right)^{2}=\frac{185}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+\frac{5}{2}\right)^{2}}=\sqrt{\frac{185}{4}}$$

Qisqartirish.

$$a+\frac{5}{2}=\frac{\sqrt{185}}{2} a+\frac{5}{2}=-\frac{\sqrt{185}}{2}$$

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

$$a=\frac{\sqrt{185}-5}{2} a=\frac{-\sqrt{185}-5}{2}$$