Whakaoti i te 0=(-0.000234)left(x-80right)^2+1.5

$$0=(-0.000234) { \left(x-80 \right) }^{ 2 } +1.5$$

Whakaoti mō x

$$x=\frac{500\sqrt{39}}{39}+80\approx 160.064076903$$

$$x=-\frac{500\sqrt{39}}{39}+80\approx -0.064076903$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-80\right)^{2}.

$$0=-0.000234\left(x^{2}-160x+6400\right)+1.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te -0.000234 ki te x^{2}-160x+6400.

$$0=-0.000234x^{2}+0.03744x-1.4976+1.5$$

Tāpirihia te -1.4976 ki te 1.5, ka 0.0024.

$$0=-0.000234x^{2}+0.03744x+0.0024$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-0.000234x^{2}+0.03744x+0.0024=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -0.000234 mō a, 0.03744 mō b, me 0.0024 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.03744±\sqrt{0.03744^{2}-4\left(-0.000234\right)\times 0.0024}}{2\left(-0.000234\right)}$$

Pūruatia 0.03744 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-0.03744±\sqrt{0.0014017536-4\left(-0.000234\right)\times 0.0024}}{2\left(-0.000234\right)}$$

Whakareatia -4 ki te -0.000234.

$$x=\frac{-0.03744±\sqrt{0.0014017536+0.000936\times 0.0024}}{2\left(-0.000234\right)}$$

Whakareatia 0.000936 ki te 0.0024 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-0.03744±\sqrt{0.0014017536+0.0000022464}}{2\left(-0.000234\right)}$$

Tāpiri 0.0014017536 ki te 0.0000022464 mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-0.03744±\sqrt{0.001404}}{2\left(-0.000234\right)}$$

Tuhia te pūtakerua o te 0.001404.

$$x=\frac{-0.03744±\frac{3\sqrt{39}}{500}}{2\left(-0.000234\right)}$$

Whakareatia 2 ki te -0.000234.

$$x=\frac{-0.03744±\frac{3\sqrt{39}}{500}}{-0.000468}$$

Nā, me whakaoti te whārite x=\frac{-0.03744±\frac{3\sqrt{39}}{500}}{-0.000468} ina he tāpiri te ±. Tāpiri -0.03744 ki te \frac{3\sqrt{39}}{500}.

$$x=\frac{\frac{3\sqrt{39}}{500}-\frac{117}{3125}}{-0.000468}$$

Whakawehe -\frac{117}{3125}+\frac{3\sqrt{39}}{500} ki te -0.000468 mā te whakarea -\frac{117}{3125}+\frac{3\sqrt{39}}{500} ki te tau huripoki o -0.000468.

$$x=-\frac{500\sqrt{39}}{39}+80$$

Nā, me whakaoti te whārite x=\frac{-0.03744±\frac{3\sqrt{39}}{500}}{-0.000468} ina he tango te ±. Tango \frac{3\sqrt{39}}{500} mai i -0.03744.

$$x=\frac{-\frac{3\sqrt{39}}{500}-\frac{117}{3125}}{-0.000468}$$

Whakawehe -\frac{117}{3125}-\frac{3\sqrt{39}}{500} ki te -0.000468 mā te whakarea -\frac{117}{3125}-\frac{3\sqrt{39}}{500} ki te tau huripoki o -0.000468.

$$x=\frac{500\sqrt{39}}{39}+80$$

Kua oti te whārite te whakatau.

$$x=-\frac{500\sqrt{39}}{39}+80 x=\frac{500\sqrt{39}}{39}+80$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-80\right)^{2}.

$$0=-0.000234\left(x^{2}-160x+6400\right)+1.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te -0.000234 ki te x^{2}-160x+6400.

$$0=-0.000234x^{2}+0.03744x-1.4976+1.5$$

Tāpirihia te -1.4976 ki te 1.5, ka 0.0024.

$$0=-0.000234x^{2}+0.03744x+0.0024$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-0.000234x^{2}+0.03744x+0.0024=0$$

Tangohia te 0.0024 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-0.000234x^{2}+0.03744x=-0.0024$$

Whakawehea ngā taha e rua o te whārite ki te -0.000234, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-0.000234x^{2}+0.03744x}{-0.000234}=-\frac{0.0024}{-0.000234}$$

Mā te whakawehe ki te -0.000234 ka wetekia te whakareanga ki te -0.000234.

$$x^{2}+\frac{0.03744}{-0.000234}x=-\frac{0.0024}{-0.000234}$$

Whakawehe 0.03744 ki te -0.000234 mā te whakarea 0.03744 ki te tau huripoki o -0.000234.

$$x^{2}-160x=-\frac{0.0024}{-0.000234}$$

Whakawehe -0.0024 ki te -0.000234 mā te whakarea -0.0024 ki te tau huripoki o -0.000234.

$$x^{2}-160x=\frac{400}{39}$$

Whakawehea te -160, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -80. Nā, tāpiria te pūrua o te -80 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-160x+\left(-80\right)^{2}=\frac{400}{39}+\left(-80\right)^{2}$$

Pūrua -80.

$$x^{2}-160x+6400=\frac{400}{39}+6400$$

Tāpiri \frac{400}{39} ki te 6400.

$$x^{2}-160x+6400=\frac{250000}{39}$$

Tauwehea te x^{2}-160x+6400. 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}.

$$\left(x-80\right)^{2}=\frac{250000}{39}$$

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

$$\sqrt{\left(x-80\right)^{2}}=\sqrt{\frac{250000}{39}}$$

Whakarūnātia.

$$x-80=\frac{500\sqrt{39}}{39} x-80=-\frac{500\sqrt{39}}{39}$$

Me tāpiri 80 ki ngā taha e rua o te whārite.

$$x=\frac{500\sqrt{39}}{39}+80 x=-\frac{500\sqrt{39}}{39}+80$$