The quadratic equation $3 x^{2} - 6 x - 18 = 0,$ can be simplified to

3 (x - 1)^{2} = 6

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(x - 3)^{2} = 6

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(x - 1)^{2} = 7

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Solution

The correct option is C $(x - 1)^{2} = 7$
Given: $3 x^{2} - 6 x - 18 = 0$
Taking $3$ common on both sides of the equation, we get:
$x^{2} - 2 x - 6 = 0$
Now, comparing the equation with $(a - b)^{2} = a^{2} - 2 a b + b^{2},$ we get:
$a = x,$ $b = 1$
Thus, $x^{2} - 2 x - 6 = 0 \Rightarrow x^{2} - 2 x + 1 - 1 - 6 = 0 \Rightarrow (x - 1)^{2} - 7 = 0 \Rightarrow (x - 1)^{2} = 7$

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Similar questions

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The quadratic equation 3x2−6x−18=0, can be simplified to

The correct option is C (x−1)2=7Given: 3x2−6x−18=0 Taking 3 common on both sides of the equation, we get: x2−2x−6=0 Now, comparing the equation with (a−b)2=a2−2ab+b2, we get: a=x, b=1 Thus, x2−2x−6=0⇒x2−2x+1−1−6=0⇒(x−1)2−7=0⇒(x−1)2=7

The quadratic equation $3 x^{2} - 6 x - 18 = 0,$ can be simplified to