Solve the quadratic equation by completing the square: x2 + 6x − 720

Question

ScanSolve AI Tutor · Accepted Answer

Sawa Dennis, twende kazi.

Ili kutatua mlinganyo wa quadratic kwa kukamilisha mraba, tunafuata hatua hizi:

Weka mlinganyo sawa na sifuri na hamisha nambari isiyo na $x$ (constant term) upande wa kulia.
Mlinganyo uliotolewa ni $x^2 + 6x - 720$ . Tunauweka sawa na sifuri:
$x^2 + 6x - 720 = 0$
Ongeza 720 pande zote mbili:
$x^2 + 6x = 720$
Kamilisha mraba upande wa kushoto.
Chukua nusu ya mgawo wa $x$ (ambayo ni 6), kisha ipandishe mraba.
Nusu ya 6 ni $\frac{6}{2} = 3$ .
Mraba wa 3 ni $3^2 = 9$ .
Ongeza 9 pande zote mbili za mlinganyo:
$x^2 + 6x + 9 = 720 + 9$
Andika upande wa kushoto kama mraba kamili na kurahisisha upande wa kulia.
$(x + 3)^2 = 729$
Chukua mzizi wa mraba pande zote mbili.
$\sqrt{(x + 3)^2} = \pm\sqrt{729}$ $x + 3 = \pm 27$
Tatua kwa $x$ .
Kuna uwezekano mbili:

Uwezekano wa kwanza:
$x + 3 = 27$
Toa 3 pande zote mbili:
$x = 27 - 3$ $x = 24$
Uwezekano wa pili:
$x + 3 = -27$
Toa 3 pande zote mbili:
$x = -27 - 3$ $x = -30$
Hivyo, suluhisho za mlinganyo ni:
$x = 24 \text{ au } x = -30$

Solve the quadratic equation by completing the square: x2 + 6x - 720