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x^{2}=\frac{256}{196}
Ikki tarafini 196 ga bo‘ling.
x^{2}=\frac{64}{49}
\frac{256}{196} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x^{2}-\frac{64}{49}=0
Ikkala tarafdan \frac{64}{49} ni ayirish.
49x^{2}-64=0
Ikkala tarafini 49 ga ko‘paytiring.
\left(7x-8\right)\left(7x+8\right)=0
Hisoblang: 49x^{2}-64. 49x^{2}-64 ni \left(7x\right)^{2}-8^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=\frac{8}{7} x=-\frac{8}{7}
Tenglamani yechish uchun 7x-8=0 va 7x+8=0 ni yeching.
x^{2}=\frac{256}{196}
Ikki tarafini 196 ga bo‘ling.
x^{2}=\frac{64}{49}
\frac{256}{196} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x=\frac{8}{7} x=-\frac{8}{7}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x^{2}=\frac{256}{196}
Ikki tarafini 196 ga bo‘ling.
x^{2}=\frac{64}{49}
\frac{256}{196} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x^{2}-\frac{64}{49}=0
Ikkala tarafdan \frac{64}{49} ni ayirish.
x=\frac{0±\sqrt{0^{2}-4\left(-\frac{64}{49}\right)}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{64}{49} ni c bilan almashtiring.
x=\frac{0±\sqrt{-4\left(-\frac{64}{49}\right)}}{2}
0 kvadratini chiqarish.
x=\frac{0±\sqrt{\frac{256}{49}}}{2}
-4 ni -\frac{64}{49} marotabaga ko'paytirish.
x=\frac{0±\frac{16}{7}}{2}
\frac{256}{49} ning kvadrat ildizini chiqarish.
x=\frac{8}{7}
x=\frac{0±\frac{16}{7}}{2} tenglamasini yeching, bunda ± musbat.
x=-\frac{8}{7}
x=\frac{0±\frac{16}{7}}{2} tenglamasini yeching, bunda ± manfiy.
x=\frac{8}{7} x=-\frac{8}{7}
Tenglama yechildi.