Whakaoti i te -b^2+26+b=0

$$- b ^ { 2 } + 26 + b = 0$$

Whakaoti mō b

$$b = \frac{\sqrt{105} + 1}{2} \approx 5.623475383$$

$$b=\frac{1-\sqrt{105}}{2}\approx -4.623475383$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-b^{2}+b+26=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 1 mō b, me 26 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

Pūrua 1.

$$b=\frac{-1±\sqrt{1-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$b=\frac{-1±\sqrt{1+4\times 26}}{2\left(-1\right)}$$

Whakareatia 4 ki te 26.

$$b=\frac{-1±\sqrt{1+104}}{2\left(-1\right)}$$

Tāpiri 1 ki te 104.

$$b=\frac{-1±\sqrt{105}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$b=\frac{-1±\sqrt{105}}{-2}$$

Nā, me whakaoti te whārite b=\frac{-1±\sqrt{105}}{-2} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{105}.

$$b=\frac{\sqrt{105}-1}{-2}$$

Whakawehe -1+\sqrt{105} ki te -2.

$$b=\frac{1-\sqrt{105}}{2}$$

Nā, me whakaoti te whārite b=\frac{-1±\sqrt{105}}{-2} ina he tango te ±. Tango \sqrt{105} mai i -1.

$$b=\frac{-\sqrt{105}-1}{-2}$$

Whakawehe -1-\sqrt{105} ki te -2.

$$b=\frac{\sqrt{105}+1}{2}$$

Kua oti te whārite te whakatau.

$$b=\frac{1-\sqrt{105}}{2} b=\frac{\sqrt{105}+1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-b^{2}+b+26=0$$

Me tango 26 mai i ngā taha e rua o te whārite.

$$-b^{2}+b+26-26=-26$$

Mā te tango i te 26 i a ia ake anō ka toe ko te 0.

$$-b^{2}+b=-26$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-b^{2}+b}{-1}=-\frac{26}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$b^{2}+\frac{1}{-1}b=-\frac{26}{-1}$$

Whakawehe 1 ki te -1.

$$b^{2}-b=-\frac{26}{-1}$$

Whakawehe -26 ki te -1.

$$b^{2}-b=26$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}-b+\left(-\frac{1}{2}\right)^{2}=26+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$b^{2}-b+\frac{1}{4}=26+\frac{1}{4}$$

Tāpiri 26 ki te \frac{1}{4}.

$$b^{2}-b+\frac{1}{4}=\frac{105}{4}$$

Tauwehea b^{2}-b+\frac{1}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(b-\frac{1}{2}\right)^{2}=\frac{105}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(b-\frac{1}{2}\right)^{2}}=\sqrt{\frac{105}{4}}$$

Whakarūnātia.

$$b-\frac{1}{2}=\frac{\sqrt{105}}{2} b-\frac{1}{2}=-\frac{\sqrt{105}}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$b=\frac{\sqrt{105}+1}{2} b=\frac{1-\sqrt{105}}{2}$$