x=-1018-9000/x eching

$$x=-1018- \frac{ 9000 }{ x }$$

x uchun yechish (complex solution)

$$x=\sqrt{250081}-509\approx -8,91900656$$

$$x=-\left(\sqrt{250081}+509\right)\approx -1009,08099344$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -1018 ni \frac{x}{x} marotabaga ko'paytirish.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

-\frac{1018x}{x} va \frac{9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$x=\frac{-1018x-9000}{x}$$

Ikkala tarafdan \frac{-1018x-9000}{x} ni ayirish.

$$x-\frac{-1018x-9000}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

\frac{xx}{x} va \frac{-1018x-9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

xx-\left(-1018x-9000\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+1018x+9000}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$x^{2}+1018x+9000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1018 ni b va 9000 ni c bilan almashtiring.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

1018 kvadratini chiqarish.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

-4 ni 9000 marotabaga ko'paytirish.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

1036324 ni -36000 ga qo'shish.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

1000324 ning kvadrat ildizini chiqarish.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

x=\frac{-1018±2\sqrt{250081}}{2} tenglamasini yeching, bunda ± musbat. -1018 ni 2\sqrt{250081} ga qo'shish.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

-1018+2\sqrt{250081} ni 2 ga bo'lish.

$$x=\sqrt{250081}-509$$

x=\frac{-1018±2\sqrt{250081}}{2} tenglamasini yeching, bunda ± manfiy. -1018 dan 2\sqrt{250081} ni ayirish.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

-1018-2\sqrt{250081} ni 2 ga bo'lish.

$$x=-\sqrt{250081}-509$$

Tenglama yechildi.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Kvadratni yakunlash bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -1018 ni \frac{x}{x} marotabaga ko'paytirish.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

-\frac{1018x}{x} va \frac{9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$x=\frac{-1018x-9000}{x}$$

Ikkala tarafdan \frac{-1018x-9000}{x} ni ayirish.

$$x-\frac{-1018x-9000}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

\frac{xx}{x} va \frac{-1018x-9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

xx-\left(-1018x-9000\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+1018x+9000}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$x^{2}+1018x+9000=0$$

Ikkala tarafdan 9000 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}+1018x=-9000$$

1018 ni bo‘lish, x shartining koeffitsienti, 2 ga 509 olish uchun. Keyin, 509 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

509 kvadratini chiqarish.

$$x^{2}+1018x+259081=-9000+259081$$

-9000 ni 259081 ga qo'shish.

$$x^{2}+1018x+259081=250081$$

x^{2}+1018x+259081 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+509\right)^{2}=250081$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Qisqartirish.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Tenglamaning ikkala tarafidan 509 ni ayirish.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

x uchun yechish

$$x=\sqrt{250081}-509\approx -8,91900656$$

$$x=-\sqrt{250081}-509\approx -1009,08099344$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -1018 ni \frac{x}{x} marotabaga ko'paytirish.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

-\frac{1018x}{x} va \frac{9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$x=\frac{-1018x-9000}{x}$$

Ikkala tarafdan \frac{-1018x-9000}{x} ni ayirish.

$$x-\frac{-1018x-9000}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

\frac{xx}{x} va \frac{-1018x-9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

xx-\left(-1018x-9000\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+1018x+9000}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$x^{2}+1018x+9000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1018 ni b va 9000 ni c bilan almashtiring.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

1018 kvadratini chiqarish.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

-4 ni 9000 marotabaga ko'paytirish.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

1036324 ni -36000 ga qo'shish.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

1000324 ning kvadrat ildizini chiqarish.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

x=\frac{-1018±2\sqrt{250081}}{2} tenglamasini yeching, bunda ± musbat. -1018 ni 2\sqrt{250081} ga qo'shish.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

-1018+2\sqrt{250081} ni 2 ga bo'lish.

$$x=\sqrt{250081}-509$$

x=\frac{-1018±2\sqrt{250081}}{2} tenglamasini yeching, bunda ± manfiy. -1018 dan 2\sqrt{250081} ni ayirish.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

-1018-2\sqrt{250081} ni 2 ga bo'lish.

$$x=-\sqrt{250081}-509$$

Tenglama yechildi.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Kvadratni yakunlash bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -1018 ni \frac{x}{x} marotabaga ko'paytirish.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

-\frac{1018x}{x} va \frac{9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$x=\frac{-1018x-9000}{x}$$

Ikkala tarafdan \frac{-1018x-9000}{x} ni ayirish.

$$x-\frac{-1018x-9000}{x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

\frac{xx}{x} va \frac{-1018x-9000}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

xx-\left(-1018x-9000\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+1018x+9000}{x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$x^{2}+1018x+9000=0$$

Ikkala tarafdan 9000 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}+1018x=-9000$$

1018 ni bo‘lish, x shartining koeffitsienti, 2 ga 509 olish uchun. Keyin, 509 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

509 kvadratini chiqarish.

$$x^{2}+1018x+259081=-9000+259081$$

-9000 ni 259081 ga qo'shish.

$$x^{2}+1018x+259081=250081$$

x^{2}+1018x+259081 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+509\right)^{2}=250081$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Qisqartirish.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Tenglamaning ikkala tarafidan 509 ni ayirish.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$