How do you solve using the completing the square method $x^{2} + 10 x + 16 = 0$ $x^2 + 10x + 16 = 0$ ?

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How do you solve using the completing the square method $x^{2} + 10 x + 16 = 0$ $x^2 + 10x + 16 = 0$ ?

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Answer 1 · 2016-02-26T09:51:10

$x = - 2$ $x=-2$ and $x = - 8$ $x=-8$

Explanation:

To solve the equation $x^{2} + 10 x + 16 = 0$ $x^2+10x+16=0$ using the completing square method, as coefficient of $x^{2}$ $x^2$ is $1$ $1$ and independent term $16$ $16$ positive, we have to identify factors of $16$ $16$ whose sum is $10$ $10$ , coefficient of $x$ $x$ term.

These are $2$ $2$ and $8$ $8$ and hence we should split the equation as follows:

$x^{2} + 2 x + 8 x + 16 = 0$ $x^2+2x+8x+16=0$ or $x (x + 2) + 8 (x + 2) = 0$ $x(x+2)+8(x+2)=0$ i.e.

$(x + 2) (x + 8) = 0$ $(x+2)(x+8)=0$ .

Hence either $x + 2 = 0$ $x+2=0$ i.e. $x = - 2$ $x=-2$ or

$x + 8 = 0$ $x+8=0$ i.e. $x = - 8$ $x=-8$

[In general if equation is in form $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ , one should identify two factors whose product is $a \cdot c$ $a*c$ and sum is $b$ $b$ .]

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How do you solve using the completing the square method $x^{2} + 10 x + 16 = 0$ $x^2 + 10x + 16 = 0$ ?

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How do you solve using the completing the square method x2+10x+16=0x^2 + 10x + 16 = 0?

1 Answer

Explanation:

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How do you solve using the completing the square method $x^{2} + 10 x + 16 = 0$ $x^2 + 10x + 16 = 0$ ?