Use the completing the square method to find the exact roots of the equation: 2x2 - 2x + 10 = 0

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ScanSolve AI Tutor · Accepted Answer

Tunatakiwa kutatua mlinganyo wa quadratic $x^2 - 12x + 10 = 0$ kwa kutumia njia ya kukamilisha mraba.

Hamisha namba isiyo na $x$ (constant term) upande wa kulia wa mlinganyo.
$x^2 - 12x = -10$
Ili kukamilisha mraba upande wa kushoto, chukua nusu ya mgawo wa $x$ (ambayo ni $-12$ ), kisha ipandishe mraba.
Mgawo wa $x$ ni $-12$ .
Nusu ya $-12$ ni $\frac{-12}{2} = -6$ .
Mraba wa $-6$ ni $(-6)^2 = 36$ .
Ongeza namba hii (36) pande zote mbili za mlinganyo.
$x^2 - 12x + 36 = -10 + 36$ $x^2 - 12x + 36 = 26$
Andika upande wa kushoto kama mraba kamili.
$(x - 6)^2 = 26$
Chukua mzizi wa mraba pande zote mbili za mlinganyo.
Kumbuka kuwa kuna majibu mawili, chanya na hasi.
$\sqrt{(x - 6)^2} = \pm\sqrt{26}$ $x - 6 = \pm\sqrt{26}$
Tatua kwa $x$ kwa kuongeza 6 pande zote mbili.
$x = 6 \pm\sqrt{26}$
Hivyo, mizizi ya mlinganyo ni:
$x_1 = 6 + \sqrt{26}$ $x_2 = 6 - \sqrt{26}$

Use the completing the square method to find the exact roots of the equation: 2x2 − 2x + 10 = 0