Whakaoti i te x^2+54x-5=500

$${ x }^{ 2 } +54x-5=500$$

Whakaoti mō x (complex solution)

$$x=\sqrt{1234}-27\approx 8.128336141$$

$$x=-\left(\sqrt{1234}+27\right)\approx -62.128336141$$

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.

$$x^{2}+54x-5=500$$

Me tango 500 mai i ngā taha e rua o te whārite.

$$x^{2}+54x-5-500=500-500$$

Mā te tango i te 500 i a ia ake anō ka toe ko te 0.

$$x^{2}+54x-5-500=0$$

Tango 500 mai i -5.

$$x^{2}+54x-505=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 54 mō b, me -505 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}$$

Pūrua 54.

$$x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}$$

Whakareatia -4 ki te -505.

$$x=\frac{-54±\sqrt{2916+2020}}{2}$$

Tāpiri 2916 ki te 2020.

$$x=\frac{-54±\sqrt{4936}}{2}$$

Tuhia te pūtakerua o te 4936.

$$x=\frac{-54±2\sqrt{1234}}{2}$$

Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tāpiri te ±. Tāpiri -54 ki te 2\sqrt{1234}.

$$x=\frac{2\sqrt{1234}-54}{2}$$

Whakawehe -54+2\sqrt{1234} ki te 2.

$$x=\sqrt{1234}-27$$

Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tango te ±. Tango 2\sqrt{1234} mai i -54.

$$x=\frac{-2\sqrt{1234}-54}{2}$$

Whakawehe -54-2\sqrt{1234} ki te 2.

$$x=-\sqrt{1234}-27$$

Kua oti te whārite te whakatau.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

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.

$$x^{2}+54x-5=500$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x^{2}+54x-5-\left(-5\right)=500-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$x^{2}+54x=500-\left(-5\right)$$

Tango -5 mai i 500.

$$x^{2}+54x=505$$

Whakawehea te 54, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 27. Nā, tāpiria te pūrua o te 27 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+54x+27^{2}=505+27^{2}$$

Pūrua 27.

$$x^{2}+54x+729=505+729$$

Tāpiri 505 ki te 729.

$$x^{2}+54x+729=1234$$

Tauwehea te x^{2}+54x+729. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+27\right)^{2}=1234$$

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

$$\sqrt{\left(x+27\right)^{2}}=\sqrt{1234}$$

Whakarūnātia.

$$x+27=\sqrt{1234} x+27=-\sqrt{1234}$$

Me tango 27 mai i ngā taha e rua o te whārite.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

Whakaoti mō x

$$x=\sqrt{1234}-27\approx 8.128336141$$

$$x=-\sqrt{1234}-27\approx -62.128336141$$

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.

$$x^{2}+54x-5=500$$

Me tango 500 mai i ngā taha e rua o te whārite.

$$x^{2}+54x-5-500=500-500$$

Mā te tango i te 500 i a ia ake anō ka toe ko te 0.

$$x^{2}+54x-5-500=0$$

Tango 500 mai i -5.

$$x^{2}+54x-505=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 54 mō b, me -505 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}$$

Pūrua 54.

$$x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}$$

Whakareatia -4 ki te -505.

$$x=\frac{-54±\sqrt{2916+2020}}{2}$$

Tāpiri 2916 ki te 2020.

$$x=\frac{-54±\sqrt{4936}}{2}$$

Tuhia te pūtakerua o te 4936.

$$x=\frac{-54±2\sqrt{1234}}{2}$$

Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tāpiri te ±. Tāpiri -54 ki te 2\sqrt{1234}.

$$x=\frac{2\sqrt{1234}-54}{2}$$

Whakawehe -54+2\sqrt{1234} ki te 2.

$$x=\sqrt{1234}-27$$

Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tango te ±. Tango 2\sqrt{1234} mai i -54.

$$x=\frac{-2\sqrt{1234}-54}{2}$$

Whakawehe -54-2\sqrt{1234} ki te 2.

$$x=-\sqrt{1234}-27$$

Kua oti te whārite te whakatau.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

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.

$$x^{2}+54x-5=500$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x^{2}+54x-5-\left(-5\right)=500-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$x^{2}+54x=500-\left(-5\right)$$

Tango -5 mai i 500.

$$x^{2}+54x=505$$

Whakawehea te 54, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 27. Nā, tāpiria te pūrua o te 27 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+54x+27^{2}=505+27^{2}$$

Pūrua 27.

$$x^{2}+54x+729=505+729$$

Tāpiri 505 ki te 729.

$$x^{2}+54x+729=1234$$

Tauwehea te x^{2}+54x+729. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+27\right)^{2}=1234$$

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

$$\sqrt{\left(x+27\right)^{2}}=\sqrt{1234}$$

Whakarūnātia.

$$x+27=\sqrt{1234} x+27=-\sqrt{1234}$$

Me tango 27 mai i ngā taha e rua o te whārite.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$