Whakaoti i te x^2/2+12^2=x^2

$$\frac { x ^ { 2 } } { 2 } + 12 ^ { 2 } = x ^ { 2 }$$

Whakaoti mō x

$$x=12\sqrt{2}\approx 16.970562748$$

$$x=-12\sqrt{2}\approx -16.970562748$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$x^{2}+2\times 12^{2}=2x^{2}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$x^{2}+2\times 144=2x^{2}$$

Whakareatia te 2 ki te 144, ka 288.

$$x^{2}+288=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}+288-2x^{2}=0$$

Pahekotia te x^{2} me -2x^{2}, ka -x^{2}.

$$-x^{2}+288=0$$

Tangohia te 288 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-x^{2}=-288$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=\frac{-288}{-1}$$

Ka taea te hautanga \frac{-288}{-1} te whakamāmā ki te 288 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=288$$

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

$$x=12\sqrt{2} x=-12\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$x^{2}+2\times 12^{2}=2x^{2}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$x^{2}+2\times 144=2x^{2}$$

Whakareatia te 2 ki te 144, ka 288.

$$x^{2}+288=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}+288-2x^{2}=0$$

Pahekotia te x^{2} me -2x^{2}, ka -x^{2}.

$$-x^{2}+288=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me 288 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 288}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 288}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\times 288}}{2\left(-1\right)}$$

Whakareatia 4 ki te 288.

$$x=\frac{0±\sqrt{1152}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 1152.

$$x=\frac{0±24\sqrt{2}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±24\sqrt{2}}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±24\sqrt{2}}{-2} ina he tāpiri te ±.

$$x=-12\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±24\sqrt{2}}{-2} ina he tango te ±.

$$x=12\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=-12\sqrt{2} x=12\sqrt{2}$$