x^2+(15x-425)=46 eching

$$x ^ { 2 } + ( 15 x - 425 ) = 46$$

x uchun yechish

$$x = \frac{\sqrt{2109} - 15}{2} \approx 15,461925006$$

$$x=\frac{-\sqrt{2109}-15}{2}\approx -30,461925006$$

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.

$$x^{2}+15x-425=46$$

Tenglamaning ikkala tarafidan 46 ni ayirish.

$$x^{2}+15x-425-46=46-46$$

O‘zidan 46 ayirilsa 0 qoladi.

$$x^{2}+15x-425-46=0$$

-425 dan 46 ni ayirish.

$$x^{2}+15x-471=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 15 ni b va -471 ni c bilan almashtiring.

$$x=\frac{-15±\sqrt{15^{2}-4\left(-471\right)}}{2}$$

15 kvadratini chiqarish.

$$x=\frac{-15±\sqrt{225-4\left(-471\right)}}{2}$$

-4 ni -471 marotabaga ko'paytirish.

$$x=\frac{-15±\sqrt{225+1884}}{2}$$

225 ni 1884 ga qo'shish.

$$x=\frac{-15±\sqrt{2109}}{2}$$

x=\frac{-15±\sqrt{2109}}{2} tenglamasini yeching, bunda ± musbat. -15 ni \sqrt{2109} ga qo'shish.

$$x=\frac{\sqrt{2109}-15}{2}$$

x=\frac{-15±\sqrt{2109}}{2} tenglamasini yeching, bunda ± manfiy. -15 dan \sqrt{2109} ni ayirish.

$$x=\frac{-\sqrt{2109}-15}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{2109}-15}{2} x=\frac{-\sqrt{2109}-15}{2}$$

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.

$$x^{2}+15x-425=46$$

425 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+15x-425-\left(-425\right)=46-\left(-425\right)$$

O‘zidan -425 ayirilsa 0 qoladi.

$$x^{2}+15x=46-\left(-425\right)$$

46 dan -425 ni ayirish.

$$x^{2}+15x=471$$

15 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{15}{2} olish uchun. Keyin, \frac{15}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+15x+\left(\frac{15}{2}\right)^{2}=471+\left(\frac{15}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{15}{2} kvadratini chiqarish.

$$x^{2}+15x+\frac{225}{4}=471+\frac{225}{4}$$

471 ni \frac{225}{4} ga qo'shish.

$$x^{2}+15x+\frac{225}{4}=\frac{2109}{4}$$

x^{2}+15x+\frac{225}{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.

$$\left(x+\frac{15}{2}\right)^{2}=\frac{2109}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{15}{2}\right)^{2}}=\sqrt{\frac{2109}{4}}$$

Qisqartirish.

$$x+\frac{15}{2}=\frac{\sqrt{2109}}{2} x+\frac{15}{2}=-\frac{\sqrt{2109}}{2}$$

Tenglamaning ikkala tarafidan \frac{15}{2} ni ayirish.

$$x=\frac{\sqrt{2109}-15}{2} x=\frac{-\sqrt{2109}-15}{2}$$