x^2-0x^2+20x-2x-16=0 eching

$$x ^ { 2 } - 0 x ^ { 2 } + 20 x - 2 x - 16 = 0$$

x uchun yechish (complex solution)

$$x=\sqrt{97}-9\approx 0,848857802$$

$$x=-\left(\sqrt{97}+9\right)\approx -18,848857802$$

Kvadrat tenglamalaridan foydalanish qoidalari

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}-0+20x-2x-16=0$$

18x ni olish uchun 20x va -2x ni birlashtirish.

$$x^{2}-0+18x-16=0$$

Shartlarni qayta saralash.

$$x^{2}+18x-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 18 ni b va -16 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

324 ni 64 ga qo'shish.

$$x=\frac{-18±\sqrt{388}}{2}$$

388 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±2\sqrt{97}}{2}$$

x=\frac{-18±2\sqrt{97}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 2\sqrt{97} ga qo'shish.

$$x=\frac{2\sqrt{97}-18}{2}$$

-18+2\sqrt{97} ni 2 ga bo'lish.

$$x=\sqrt{97}-9$$

x=\frac{-18±2\sqrt{97}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 2\sqrt{97} ni ayirish.

$$x=\frac{-2\sqrt{97}-18}{2}$$

-18-2\sqrt{97} ni 2 ga bo'lish.

$$x=-\sqrt{97}-9$$

Tenglama yechildi.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Kvadratni yakunlash bo'yicha qadamlar

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}-0+20x-2x-16=0$$

18x ni olish uchun 20x va -2x ni birlashtirish.

$$x^{2}-0+18x-16=0$$

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

$$x^{2}-0+18x=16$$

Shartlarni qayta saralash.

$$x^{2}+18x=16$$

18 ni bo‘lish, x shartining koeffitsienti, 2 ga 9 olish uchun. Keyin, 9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+18x+9^{2}=16+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=16+81$$

16 ni 81 ga qo'shish.

$$x^{2}+18x+81=97$$

x^{2}+18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+9\right)^{2}=97$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Qisqartirish.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

x uchun yechish

$$x=\sqrt{97}-9\approx 0,848857802$$

$$x=-\sqrt{97}-9\approx -18,848857802$$

Kvadrat tenglamalaridan foydalanish qoidalari

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}-0+20x-2x-16=0$$

18x ni olish uchun 20x va -2x ni birlashtirish.

$$x^{2}-0+18x-16=0$$

Shartlarni qayta saralash.

$$x^{2}+18x-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 18 ni b va -16 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

324 ni 64 ga qo'shish.

$$x=\frac{-18±\sqrt{388}}{2}$$

388 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±2\sqrt{97}}{2}$$

x=\frac{-18±2\sqrt{97}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 2\sqrt{97} ga qo'shish.

$$x=\frac{2\sqrt{97}-18}{2}$$

-18+2\sqrt{97} ni 2 ga bo'lish.

$$x=\sqrt{97}-9$$

x=\frac{-18±2\sqrt{97}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 2\sqrt{97} ni ayirish.

$$x=\frac{-2\sqrt{97}-18}{2}$$

-18-2\sqrt{97} ni 2 ga bo'lish.

$$x=-\sqrt{97}-9$$

Tenglama yechildi.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Kvadratni yakunlash bo'yicha qadamlar

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}-0+20x-2x-16=0$$

18x ni olish uchun 20x va -2x ni birlashtirish.

$$x^{2}-0+18x-16=0$$

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

$$x^{2}-0+18x=16$$

Shartlarni qayta saralash.

$$x^{2}+18x=16$$

18 ni bo‘lish, x shartining koeffitsienti, 2 ga 9 olish uchun. Keyin, 9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+18x+9^{2}=16+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=16+81$$

16 ni 81 ga qo'shish.

$$x^{2}+18x+81=97$$

x^{2}+18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+9\right)^{2}=97$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Qisqartirish.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$