Whakaoti i te 7x+x^2=(x^2+14x+48)div2

$$7x+ { x }^{ 2 } =( { x }^{ 2 } +14x+48) \div 2$$

Whakaoti mō x

$$x=4\sqrt{3}\approx 6.92820323$$

$$x=-4\sqrt{3}\approx -6.92820323$$

Ngā Upane mā te Kimi Pūtakerua

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

$$14x+2x^{2}=x^{2}+14x+48$$

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

$$14x+2x^{2}-x^{2}=14x+48$$

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

$$14x+x^{2}=14x+48$$

Tangohia te 14x mai i ngā taha e rua.

$$14x+x^{2}-14x=48$$

Pahekotia te 14x me -14x, ka 0.

$$x^{2}=48$$

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

$$x=4\sqrt{3} x=-4\sqrt{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$14x+2x^{2}=x^{2}+14x+48$$

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

$$14x+2x^{2}-x^{2}=14x+48$$

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

$$14x+x^{2}=14x+48$$

Tangohia te 14x mai i ngā taha e rua.

$$14x+x^{2}-14x=48$$

Pahekotia te 14x me -14x, ka 0.

$$x^{2}=48$$

Tangohia te 48 mai i ngā taha e rua.

$$x^{2}-48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-48\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-48\right)}}{2}$$

Whakareatia -4 ki te -48.

$$x=\frac{0±\sqrt{192}}{2}$$

Tuhia te pūtakerua o te 192.

$$x=\frac{0±8\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{3}}{2} ina he tāpiri te ±.

$$x=4\sqrt{3}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{3}}{2} ina he tango te ±.

$$x=-4\sqrt{3}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{3} x=-4\sqrt{3}$$