x uchun yechish
x=\sqrt{23}+9\approx 13,795831523
x=9-\sqrt{23}\approx 4,204168477
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}-18x+58=0x^{2}
0 hosil qilish uchun 0 va 4 ni ko'paytirish.
x^{2}-18x+58=0
Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.
x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 58}}{2}
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 58 ni c bilan almashtiring.
x=\frac{-\left(-18\right)±\sqrt{324-4\times 58}}{2}
-18 kvadratini chiqarish.
x=\frac{-\left(-18\right)±\sqrt{324-232}}{2}
-4 ni 58 marotabaga ko'paytirish.
x=\frac{-\left(-18\right)±\sqrt{92}}{2}
324 ni -232 ga qo'shish.
x=\frac{-\left(-18\right)±2\sqrt{23}}{2}
92 ning kvadrat ildizini chiqarish.
x=\frac{18±2\sqrt{23}}{2}
-18 ning teskarisi 18 ga teng.
x=\frac{2\sqrt{23}+18}{2}
x=\frac{18±2\sqrt{23}}{2} tenglamasini yeching, bunda ± musbat. 18 ni 2\sqrt{23} ga qo'shish.
x=\sqrt{23}+9
18+2\sqrt{23} ni 2 ga bo'lish.
x=\frac{18-2\sqrt{23}}{2}
x=\frac{18±2\sqrt{23}}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 2\sqrt{23} ni ayirish.
x=9-\sqrt{23}
18-2\sqrt{23} ni 2 ga bo'lish.
x=\sqrt{23}+9 x=9-\sqrt{23}
Tenglama yechildi.
x^{2}-18x+58=0x^{2}
0 hosil qilish uchun 0 va 4 ni ko'paytirish.
x^{2}-18x+58=0
Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.
x^{2}-18x=-58
Ikkala tarafdan 58 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.
x^{2}-18x+\left(-9\right)^{2}=-58+\left(-9\right)^{2}
-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+81=-58+81
-9 kvadratini chiqarish.
x^{2}-18x+81=23
-58 ni 81 ga qo'shish.
\left(x-9\right)^{2}=23
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.
\sqrt{\left(x-9\right)^{2}}=\sqrt{23}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-9=\sqrt{23} x-9=-\sqrt{23}
Qisqartirish.
x=\sqrt{23}+9 x=9-\sqrt{23}
9 ni tenglamaning ikkala tarafiga qo'shish.
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