How do you solve using the completing the square method $x^{2} + 2 x = 0$ $x^2 + 2x = 0$ ?

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How do you solve using the completing the square method $x^{2} + 2 x = 0$ $x^2 + 2x = 0$ ?

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Answer 1 · 2016-03-22T05:36:56

Please follow the process given below. Answer is $x = 0$ $x=0$ and $x = - 2$ $x=-2$

Explanation:

We know that ${(x + a)}^{2} = x^{2} + 2 a x + a^{2}$ $(x+a)^2=x^2+2ax+a^2$ , hence to complete say $x^{2} + b x$ $x^2+bx$ to a square we should add and subtract, square of half the coefficient of $x$ $x$ i.e. ${(\frac{b}{2})}^{2}$ $(b/2)^2$ .

As the equation is $x^{2} + 2 x = 0$ $x^2+2x=0$ , we have to add and subtract ${(\frac{2}{2})}^{2} = 1$ $(2/2)^2=1$ and equation becomes

$x^{2} + 2 x + 1 - 1 = 0$ $x^2+2x+1-1=0$ and now this can be written as

${(x + 1)}^{2} - 1 = 0$ $(x+1)^2-1=0$ or

$((x + 1) + 1) \times ((x + 1) - 1) = 0$ $((x+1)+1)xx((x+1)-1)=0$ or

$((x + 2) \times x = 0$ $((x+2)xx x=0$ i.e. either $x = 0$ $x=0$ or $x + 2 = 0$ $x+2=0$ or $x = - 2$ $x=-2$

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How do you solve using the completing the square method $x^{2} + 2 x = 0$ $x^2 + 2x = 0$ ?

1 Answer

Explanation:

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How do you solve using the completing the square method $x^{2} + 2 x = 0$ $x^2 + 2x = 0$ ?