Whakaoti i te 003=2xleft(1-100/sqrt{996*10^6}right)-1

$$003 = 2x \left( 1- \frac{ 100 }{ \sqrt{ 996 \times { 10 }^{ 6 } } } \right) -1$$

Whakaoti mō x

$$x=\frac{10\left(\sqrt{249}+4980\right)}{99599}\approx 0.501589347$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 0 ki te 0, ka 0.

$$0\times 3=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

Whakareatia te 0 ki te 3, ka 0.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

Tātaihia te 10 mā te pū o 6, kia riro ko 1000000.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 1000000}}\right)-1$$

Whakareatia te 996 ki te 1000000, ka 996000000.

$$0=2x\left(1-\frac{100}{\sqrt{996000000}}\right)-1$$

Tauwehea te 996000000=2000^{2}\times 249. Tuhia anō te pūtake rua o te hua \sqrt{2000^{2}\times 249} hei hua o ngā pūtake rua \sqrt{2000^{2}}\sqrt{249}. Tuhia te pūtakerua o te 2000^{2}.

$$0=2x\left(1-\frac{100}{2000\sqrt{249}}\right)-1$$

Whakangāwaritia te tauraro o \frac{100}{2000\sqrt{249}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{249}.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

Ko te pūrua o \sqrt{249} ko 249.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\times 249}\right)-1$$

Me whakakore tahi te 100 i te taurunga me te tauraro.

$$0=2x\left(1-\frac{\sqrt{249}}{20\times 249}\right)-1$$

Whakareatia te 20 ki te 249, ka 4980.

$$0=2x\left(1-\frac{\sqrt{249}}{4980}\right)-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 1-\frac{\sqrt{249}}{4980}.

$$0=2x+2x\left(-\frac{\sqrt{249}}{4980}\right)-1$$

Whakakorea atu te tauwehe pūnoa nui rawa 4980 i roto i te 2 me te 4980.

$$0=2x+\frac{\sqrt{249}}{-2490}x-1$$

Tuhia te \frac{\sqrt{249}}{-2490}x hei hautanga kotahi.

$$0=2x+\frac{\sqrt{249}x}{-2490}-1$$

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

$$2x+\frac{\sqrt{249}x}{-2490}-1=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2x+\frac{\sqrt{249}x}{-2490}=1$$

Whakareatia ngā taha e rua o te whārite ki te -2490.

$$-4980x+\sqrt{249}x=-2490$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-4980+\sqrt{249}\right)x=-2490$$

He hanga arowhānui tō te whārite.

$$\left(\sqrt{249}-4980\right)x=-2490$$

Whakawehea ngā taha e rua ki te -4980+\sqrt{249}.

$$\frac{\left(\sqrt{249}-4980\right)x}{\sqrt{249}-4980}=-\frac{2490}{\sqrt{249}-4980}$$

Mā te whakawehe ki te -4980+\sqrt{249} ka wetekia te whakareanga ki te -4980+\sqrt{249}.

$$x=-\frac{2490}{\sqrt{249}-4980}$$

Whakawehe -2490 ki te -4980+\sqrt{249}.

$$x=\frac{10\sqrt{249}+49800}{99599}$$