Solve the quadratic equation x2 -by the method of completing the square-

Given: nbsp; x^2 + 4x +2 = 0 This is same as: x^2+[ 2 × (x) × 2]+ 2^2 – 2^2 +2 = 0 ⇒ (x +2)^2 – 2 = 0 ⇒ nbsp;(x + 2)^2 – 2 = 0 ⇒ nbsp;(x + 2)^2 = 2 ⇒ x +2 ...

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Standard X

Mathematics

Formation of Quadratic Equation from Roots

Solve the qua...

Question

Solve the quadratic equation $x^{2} + 4 x + 2 = 0$ by the method of completing the square.

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Solution

Given: $x^{2} + 4 x + 2 = 0$
This is same as:
$x^{2} + [2 \times (x) \times 2] + 2^{2} - 2^{2} + 2 = 0$
$\Rightarrow (x + 2)^{2} - 2 = 0$
$\Rightarrow (x + 2)^{2} - 2 = 0$
$\Rightarrow (x + 2)^{2} = 2$
$\Rightarrow x + 2 = \pm \sqrt{2}$
$\Rightarrow x = - 2 \pm \sqrt{2}$

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Solve the quadratic equation x2+4x+2=0by the method of completing the square.

Given: x2+4x+2=0 This is same as: x2+[2×(x)×2]+22–22+2=0 ⇒(x+2)2–2=0 ⇒(x+2)2–2=0 ⇒(x+2)2=2 ⇒x+2=±√2 ⇒x=−2±√2

Solve the quadratic equation $x^{2} + 4 x + 2 = 0$ by the method of completing the square.

Given: $x^{2} + 4 x + 2 = 0$
This is same as:
$x^{2} + [2 \times (x) \times 2] + 2^{2} - 2^{2} + 2 = 0$
$\Rightarrow (x + 2)^{2} - 2 = 0$
$\Rightarrow (x + 2)^{2} - 2 = 0$
$\Rightarrow (x + 2)^{2} = 2$
$\Rightarrow x + 2 = \pm \sqrt{2}$
$\Rightarrow x = - 2 \pm \sqrt{2}$