913=81+x^2-8x eching

$$913 = 81 + x ^ { 2 } - 8 x$$

x uchun yechish

$$x=4\sqrt{53}+4\approx 33,120439557$$

$$x=4-4\sqrt{53}\approx -25,120439557$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$81+x^{2}-8x=913$$

Ikkala tarafdan 913 ni ayirish.

$$81+x^{2}-8x-913=0$$

-832 olish uchun 81 dan 913 ni ayirish.

$$-832+x^{2}-8x=0$$

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.

$$x^{2}-8x-832=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va -832 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-832\right)}}{2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-832\right)}}{2}$$

-4 ni -832 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+3328}}{2}$$

64 ni 3328 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{3392}}{2}$$

3392 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±8\sqrt{53}}{2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±8\sqrt{53}}{2}$$

x=\frac{8±8\sqrt{53}}{2} tenglamasini yeching, bunda ± musbat. 8 ni 8\sqrt{53} ga qo'shish.

$$x=\frac{8\sqrt{53}+8}{2}$$

8+8\sqrt{53} ni 2 ga bo'lish.

$$x=4\sqrt{53}+4$$

x=\frac{8±8\sqrt{53}}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 8\sqrt{53} ni ayirish.

$$x=\frac{8-8\sqrt{53}}{2}$$

8-8\sqrt{53} ni 2 ga bo'lish.

$$x=4-4\sqrt{53}$$

Tenglama yechildi.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$81+x^{2}-8x=913$$

Ikkala tarafdan 81 ni ayirish.

$$x^{2}-8x=913-81$$

832 olish uchun 913 dan 81 ni ayirish.

$$x^{2}-8x=832$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=832+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=832+16$$

832 ni 16 ga qo'shish.

$$x^{2}-8x+16=848$$

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-4\right)^{2}=848$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{848}$$

Qisqartirish.

$$x-4=4\sqrt{53} x-4=-4\sqrt{53}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$