Lutasin ang x^2/(4-x)(1-x)=13*10^9

$$\frac { x ^ { 2 } } { ( 4 - x ) ( 1 - x ) } = 13 \times 10 ^ { 9 }$$

I-solve ang x

$$x = \frac{20000 \sqrt{950625000130} + 32500000000}{12999999999} \approx 4$$

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}\approx 1$$

Mga Hakbang sa Paggamit ng Quadratic Formula

Ang variable x ay hindi katumbas ng anuman sa mga value na 1,4 dahil hindi tukoy ang division by zero. I-multiply ang magkabilang dulo ng equation gamit ang \left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Kalkulahin ang 10 sa power ng 9 at kunin ang 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

I-multiply ang 13 at 1000000000 para makuha ang 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Gamitin ang distributive property para i-multiply ang 13000000000 gamit ang x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Gamitin ang distributive property para i-multiply ang 13000000000x-52000000000 sa x-1 at para pagsamahin ang magkakatulad na term.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

I-subtract ang 13000000000x^{2} mula sa magkabilang dulo.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Pagsamahin ang x^{2} at -13000000000x^{2} para makuha ang -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Idagdag ang 65000000000x sa parehong bahagi.

$$-12999999999x^{2}[phone]x=52000000000$$

I-subtract ang 52000000000 mula sa magkabilang dulo.

$$-12999999999x^{2}[phone]x-52000000000=0$$

Ang equation ay nasa standard form: ax^{2}+bx+c=0. I-substitute ang -12999999999 para sa a, 65000000000 para sa b, at -52000000000 para sa c sa quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-65000000000±\sqrt{65000000000^{2}-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

I-square ang 65000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

I-multiply ang -4 times -12999999999.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000+51999999996\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

I-multiply ang 51999999996 times -52000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-2703999999792000000000}}{2\left(-12999999999\right)}$$

Idagdag ang 4225000000000000000000 sa -2703999999792000000000.

$$x=\frac{-65000000000±\sqrt{1521000000208000000000}}{2\left(-12999999999\right)}$$

Kunin ang square root ng 1521000000208000000000.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{2\left(-12999999999\right)}$$

I-multiply ang 2 times -12999999999.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998}$$

Ngayon, lutasin ang equation na x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} kapag ang ± ay plus. Idagdag ang -65000000000 sa 40000\sqrt{950625000130}.

$$x=\frac{40000\sqrt{950625000130}-65000000000}{-25999999998}$$

I-divide ang -65000000000+40000\sqrt{950625000130} gamit ang -25999999998.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$

Ngayon, lutasin ang equation na x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} kapag ang ± ay minus. I-subtract ang 40000\sqrt{950625000130} mula sa -65000000000.

$$x=\frac{-40000\sqrt{950625000130}-65000000000}{-25999999998}$$

I-divide ang -65000000000-40000\sqrt{950625000130} gamit ang -25999999998.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

Nalutas na ang equation.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999} x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

Mga Hakbang sa Pagkukumpleto sa Square

Ang variable x ay hindi katumbas ng anuman sa mga value na 1,4 dahil hindi tukoy ang division by zero. I-multiply ang magkabilang dulo ng equation gamit ang \left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Kalkulahin ang 10 sa power ng 9 at kunin ang 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

I-multiply ang 13 at 1000000000 para makuha ang 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Gamitin ang distributive property para i-multiply ang 13000000000 gamit ang x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Gamitin ang distributive property para i-multiply ang 13000000000x-52000000000 sa x-1 at para pagsamahin ang magkakatulad na term.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

I-subtract ang 13000000000x^{2} mula sa magkabilang dulo.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Pagsamahin ang x^{2} at -13000000000x^{2} para makuha ang -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Idagdag ang 65000000000x sa parehong bahagi.

$$-12999999999x^{2}[phone]x=52000000000$$

I-divide ang magkabilang dulo ng equation gamit ang -12999999999.

$$\frac{-12999999999x^{2}[phone]x}{-12999999999}=\frac{52000000000}{-12999999999}$$

Kapag na-divide gamit ang -12999999999, ma-a-undo ang multiplication gamit ang -12999999999.

$$x^{2}+\frac{65000000000}{-12999999999}x=\frac{52000000000}{-12999999999}$$

I-divide ang 65000000000 gamit ang -12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=\frac{52000000000}{-12999999999}$$

I-divide ang 52000000000 gamit ang -12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=-\frac{52000000000}{12999999999}$$

I-divide ang -\frac{65000000000}{12999999999}, ang coefficient ng x term, gamit ang 2 para makuha ang -\frac{32500000000}{12999999999}. Pagkatapos ay idagdag ang square ng -\frac{32500000000}{12999999999} sa magkabilang panig ng equation. Kapag ginawa ang hakbang na ito, magiging perfect square ang kaliwang panig ng equation.

$$x^{2}-\frac{65000000000}{12999999999}x+\left(-\frac{32500000000}{12999999999}\right)^{2}=-\frac{52000000000}{12999999999}+\left(-\frac{32500000000}{12999999999}\right)^{2}$$

I-square ang -\frac{32500000000}{12999999999} sa pamamagitan ng pagse-square sa numerator at denominator ng fraction.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=-\frac{52000000000}{12999999999}+\frac{1056250000000000000000}{168999999974000000001}$$

Idagdag ang -\frac{52000000000}{12999999999} sa \frac{1056250000000000000000}{168999999974000000001} sa pamamagitan ng paghahanap ng common denominator at pagdadagdag sa mga numerator. Pagkatapos ay ibawas ang fraction sa lowest terms nito kung posible.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=\frac{380250000052000000000}{168999999974000000001}$$

I-factor ang x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}. Sa pangkalahatan, kapag ang x^{2}+bx+c ay perfect square, maaari itong palaging i-factor bilang \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{32500000000}{12999999999}\right)^{2}=\frac{380250000052000000000}{168999999974000000001}$$

Kunin ang square root ng magkabilang dulo ng equation.

$$\sqrt{\left(x-\frac{32500000000}{12999999999}\right)^{2}}=\sqrt{\frac{380250000052000000000}{168999999974000000001}}$$

Pasimplehin.

$$x-\frac{32500000000}{12999999999}=\frac{20000\sqrt{950625000130}}{12999999999} x-\frac{32500000000}{12999999999}=-\frac{20000\sqrt{950625000130}}{12999999999}$$

Idagdag ang \frac{32500000000}{12999999999} sa magkabilang dulo ng equation.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999} x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$