Whakaoti i te (2x-5)^2=(x+3)(4x-8)

$$( 2 x - 5 ) ^ { 2 } = ( x + 3 ) ( 4 x - 8 )$$

Whakaoti mō x

$$x = \frac{49}{24} = 2\frac{1}{24} \approx 2.041666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-20x+25=\left(x+3\right)\left(4x-8\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te 4x-8 ka whakakotahi i ngā kupu rite.

$$4x^{2}-20x+25=4x^{2}+4x-24$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$4x^{2}-20x+25-4x^{2}=4x-24$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-20x+25=4x-24$$

Tangohia te 4x mai i ngā taha e rua.

$$-20x+25-4x=-24$$

Pahekotia te -20x me -4x, ka -24x.

$$-24x+25=-24$$

Tangohia te 25 mai i ngā taha e rua.

$$-24x=-24-25$$

Tangohia te 25 i te -24, ka -49.

$$-24x=-49$$

Whakawehea ngā taha e rua ki te -24.

$$x=\frac{-49}{-24}$$

Ka taea te hautanga \frac{-49}{-24} te whakamāmā ki te \frac{49}{24} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{49}{24}$$