18=-1/5x^2-12x+32 eching

$$18 = - \frac { 1 } { 5 } x ^ { 2 } - 12 x + 32$$

x uchun yechish (complex solution)

$$x=\sqrt{970}-30\approx 1,144823005$$

$$x=-\left(\sqrt{970}+30\right)\approx -61,144823005$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-\frac{1}{5}x^{2}-12x+32=18$$

Ikkala tarafdan 18 ni ayirish.

$$-\frac{1}{5}x^{2}-12x+32-18=0$$

14 olish uchun 32 dan 18 ni ayirish.

$$-\frac{1}{5}x^{2}-12x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{1}{5} ni a, -12 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

-4 ni -\frac{1}{5} marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+\frac{4}{5}\times 14}}{2\left(-\frac{1}{5}\right)}$$

\frac{4}{5} ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+\frac{56}{5}}}{2\left(-\frac{1}{5}\right)}$$

144 ni \frac{56}{5} ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{\frac{776}{5}}}{2\left(-\frac{1}{5}\right)}$$

\frac{776}{5} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±\frac{2\sqrt{970}}{5}}{2\left(-\frac{1}{5}\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±\frac{2\sqrt{970}}{5}}{2\left(-\frac{1}{5}\right)}$$

2 ni -\frac{1}{5} marotabaga ko'paytirish.

$$x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}}$$

x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± musbat. 12 ni \frac{2\sqrt{970}}{5} ga qo'shish.

$$x=\frac{\frac{2\sqrt{970}}{5}+12}{-\frac{2}{5}}$$

12+\frac{2\sqrt{970}}{5} ni -\frac{2}{5} ga bo'lish 12+\frac{2\sqrt{970}}{5} ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=-\left(\sqrt{970}+30\right)$$

x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± manfiy. 12 dan \frac{2\sqrt{970}}{5} ni ayirish.

$$x=\frac{-\frac{2\sqrt{970}}{5}+12}{-\frac{2}{5}}$$

12-\frac{2\sqrt{970}}{5} ni -\frac{2}{5} ga bo'lish 12-\frac{2\sqrt{970}}{5} ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=\sqrt{970}-30$$

Tenglama yechildi.

$$x=-\left(\sqrt{970}+30\right) x=\sqrt{970}-30$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-\frac{1}{5}x^{2}-12x+32=18$$

Ikkala tarafdan 32 ni ayirish.

$$-\frac{1}{5}x^{2}-12x=18-32$$

-14 olish uchun 18 dan 32 ni ayirish.

$$-\frac{1}{5}x^{2}-12x=-14$$

Ikkala tarafini -5 ga ko‘paytiring.

$$\frac{-\frac{1}{5}x^{2}-12x}{-\frac{1}{5}}=-\frac{14}{-\frac{1}{5}}$$

-\frac{1}{5} ga bo'lish -\frac{1}{5} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{-\frac{1}{5}}\right)x=-\frac{14}{-\frac{1}{5}}$$

-12 ni -\frac{1}{5} ga bo'lish -12 ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}+60x=-\frac{14}{-\frac{1}{5}}$$

-14 ni -\frac{1}{5} ga bo'lish -14 ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}+60x=70$$

60 ni bo‘lish, x shartining koeffitsienti, 2 ga 30 olish uchun. Keyin, 30 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+60x+30^{2}=70+30^{2}$$

30 kvadratini chiqarish.

$$x^{2}+60x+900=70+900$$

70 ni 900 ga qo'shish.

$$x^{2}+60x+900=970$$

x^{2}+60x+900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+30\right)^{2}=970$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+30\right)^{2}}=\sqrt{970}$$

Qisqartirish.

$$x+30=\sqrt{970} x+30=-\sqrt{970}$$

Tenglamaning ikkala tarafidan 30 ni ayirish.

$$x=\sqrt{970}-30 x=-\sqrt{970}-30$$

x uchun yechish

$$x=\sqrt{970}-30\approx 1,144823005$$

$$x=-\sqrt{970}-30\approx -61,144823005$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-\frac{1}{5}x^{2}-12x+32=18$$

Ikkala tarafdan 18 ni ayirish.

$$-\frac{1}{5}x^{2}-12x+32-18=0$$

14 olish uchun 32 dan 18 ni ayirish.

$$-\frac{1}{5}x^{2}-12x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{1}{5} ni a, -12 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

-4 ni -\frac{1}{5} marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+\frac{4}{5}\times 14}}{2\left(-\frac{1}{5}\right)}$$

\frac{4}{5} ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+\frac{56}{5}}}{2\left(-\frac{1}{5}\right)}$$

144 ni \frac{56}{5} ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{\frac{776}{5}}}{2\left(-\frac{1}{5}\right)}$$

\frac{776}{5} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±\frac{2\sqrt{970}}{5}}{2\left(-\frac{1}{5}\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±\frac{2\sqrt{970}}{5}}{2\left(-\frac{1}{5}\right)}$$

2 ni -\frac{1}{5} marotabaga ko'paytirish.

$$x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}}$$

x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± musbat. 12 ni \frac{2\sqrt{970}}{5} ga qo'shish.

$$x=\frac{\frac{2\sqrt{970}}{5}+12}{-\frac{2}{5}}$$

12+\frac{2\sqrt{970}}{5} ni -\frac{2}{5} ga bo'lish 12+\frac{2\sqrt{970}}{5} ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=-\left(\sqrt{970}+30\right)$$

x=\frac{12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± manfiy. 12 dan \frac{2\sqrt{970}}{5} ni ayirish.

$$x=\frac{-\frac{2\sqrt{970}}{5}+12}{-\frac{2}{5}}$$

12-\frac{2\sqrt{970}}{5} ni -\frac{2}{5} ga bo'lish 12-\frac{2\sqrt{970}}{5} ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=\sqrt{970}-30$$

Tenglama yechildi.

$$x=-\left(\sqrt{970}+30\right) x=\sqrt{970}-30$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-\frac{1}{5}x^{2}-12x+32=18$$

Ikkala tarafdan 32 ni ayirish.

$$-\frac{1}{5}x^{2}-12x=18-32$$

-14 olish uchun 18 dan 32 ni ayirish.

$$-\frac{1}{5}x^{2}-12x=-14$$

Ikkala tarafini -5 ga ko‘paytiring.

$$\frac{-\frac{1}{5}x^{2}-12x}{-\frac{1}{5}}=-\frac{14}{-\frac{1}{5}}$$

-\frac{1}{5} ga bo'lish -\frac{1}{5} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{-\frac{1}{5}}\right)x=-\frac{14}{-\frac{1}{5}}$$

-12 ni -\frac{1}{5} ga bo'lish -12 ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}+60x=-\frac{14}{-\frac{1}{5}}$$

-14 ni -\frac{1}{5} ga bo'lish -14 ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}+60x=70$$

60 ni bo‘lish, x shartining koeffitsienti, 2 ga 30 olish uchun. Keyin, 30 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+60x+30^{2}=70+30^{2}$$

30 kvadratini chiqarish.

$$x^{2}+60x+900=70+900$$

70 ni 900 ga qo'shish.

$$x^{2}+60x+900=970$$

x^{2}+60x+900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+30\right)^{2}=970$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+30\right)^{2}}=\sqrt{970}$$

Qisqartirish.

$$x+30=\sqrt{970} x+30=-\sqrt{970}$$

Tenglamaning ikkala tarafidan 30 ni ayirish.

$$x=\sqrt{970}-30 x=-\sqrt{970}-30$$