x^2+5x-30=0 eching

$${ x }^{ 2 } +5x-30=0$$

x uchun yechish

$$x = \frac{\sqrt{145} - 5}{2} \approx 3,520797289$$

$$x=\frac{-\sqrt{145}-5}{2}\approx -8,520797289$$

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.

$$x^{2}+5x-30=0$$

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 -30 ni c bilan almashtiring.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-30\right)}}{2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-30\right)}}{2}$$

-4 ni -30 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+120}}{2}$$

25 ni 120 ga qo'shish.

$$x=\frac{-5±\sqrt{145}}{2}$$

x=\frac{-5±\sqrt{145}}{2} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{145} ga qo'shish.

$$x=\frac{\sqrt{145}-5}{2}$$

x=\frac{-5±\sqrt{145}}{2} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{145} ni ayirish.

$$x=\frac{-\sqrt{145}-5}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{145}-5}{2} x=\frac{-\sqrt{145}-5}{2}$$

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.

$$x^{2}+5x-30=0$$

30 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+5x-30-\left(-30\right)=-\left(-30\right)$$

O‘zidan -30 ayirilsa 0 qoladi.

$$x^{2}+5x=-\left(-30\right)$$

0 dan -30 ni ayirish.

$$x^{2}+5x=30$$

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.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=30+\left(\frac{5}{2}\right)^{2}$$

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

$$x^{2}+5x+\frac{25}{4}=30+\frac{25}{4}$$

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

$$x^{2}+5x+\frac{25}{4}=\frac{145}{4}$$

x^{2}+5x+\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.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{145}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{145}{4}}$$

Qisqartirish.

$$x+\frac{5}{2}=\frac{\sqrt{145}}{2} x+\frac{5}{2}=-\frac{\sqrt{145}}{2}$$

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

$$x=\frac{\sqrt{145}-5}{2} x=\frac{-\sqrt{145}-5}{2}$$