What does completing the square mean?

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What does completing the square mean?

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Answer 1 · 2014-09-16T01:18:45

Completing the square is a method that represents a quadratic equation as a combination of quadrilateral used to form a square.

The basis of this method is to discover a special value that when added to both sides of the quadratic that will create a perfect square trinomial.

That special value is found by evaluation the expression ${(\frac{b}{2})}^{2}$ $(b/2)^2$ where $b$ $b$ is found in $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ . Also in this explanation I assume that $a$ $a$ has a value of $1$ $1$ .

$a x^{2} + b x + {(\frac{b}{2})}^{2} = {(\frac{b}{2})}^{2} - c$ $ax^2+bx+(b/2)^2=(b/2)^2-c$

${(a x + \frac{b}{2})}^{2} = {(\frac{b}{2})}^{2} - c$ $(ax+b/2)^2=(b/2)^2-c$

$\sqrt{{(a x + \frac{b}{2})}^{2}} = \pm \sqrt{{(\frac{b}{2})}^{2} - c}$ $sqrt((ax+b/2)^2)=+-sqrt((b/2)^2-c)$

$a x + \frac{b}{2} = \pm \sqrt{{(\frac{b}{2})}^{2} - c}$ $ax+b/2=+-sqrt((b/2)^2-c)$

$a x = \pm \sqrt{{(\frac{b}{2})}^{2} - c} - \frac{b}{2}$ $ax=+-sqrt((b/2)^2-c)-b/2$

A quadratic that is a perfect square is very easy to solve.

Please take a look at the video to see an example of completing the square visually.

Completing the Square

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What does completing the square mean?

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