Solution 2.3:5a

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In this exercise we can use the technique for writing equations in factorized form. Consider in our case the equation
In this exercise we can use the technique for writing equations in factorized form. Consider in our case the equation
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{{Displayed math||<math>(x+7)(x+7)=0\,\textrm{.}</math>}}
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<math>\left( x+7 \right)\left( x+7 \right)=0</math>
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This equation has only <math>x=-7</math> as a root because both factors become zero only when <math>x=-7</math>. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded,
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{{Displayed math||<math>(x+7)(x+7) = x^{2}+14x+49\,\textrm{.}</math>}}
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This equation has only
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<math>x=-\text{7}</math>
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as a root because both factors become zero only when
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<math>x=-\text{7}</math>. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded:
+
 +
Thus, one answer is the equation <math>x^{2}+14x+49=0\,</math>.
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<math>\left( x+7 \right)\left( x+7 \right)=x^{2}+14x+49</math>
 
 +
Note: All second-degree equations which have <math>x=-7</math> as its sole root can be written as
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Thus, one answer is the equation
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{{Displayed math||<math>ax^{2}+14ax+49a=0\,,</math>}}
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<math>x^{2}+14x+49=0</math>.
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NOTE: All second-degree equations which have
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where ''a'' is a non-zero constant.
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<math>x=-\text{7}</math>
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as a root can be written as
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+
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+
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<math>ax^{2}+14ax+49a=0</math>
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where
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<math>a</math>
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is a non-zero constant.
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Current revision

In this exercise we can use the technique for writing equations in factorized form. Consider in our case the equation

\displaystyle (x+7)(x+7)=0\,\textrm{.}

This equation has only \displaystyle x=-7 as a root because both factors become zero only when \displaystyle x=-7. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded,

\displaystyle (x+7)(x+7) = x^{2}+14x+49\,\textrm{.}

Thus, one answer is the equation \displaystyle x^{2}+14x+49=0\,.


Note: All second-degree equations which have \displaystyle x=-7 as its sole root can be written as

\displaystyle ax^{2}+14ax+49a=0\,,

where a is a non-zero constant.

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