Respuesta :
we are given the following expression:
[tex]x^2+12x+25=17[/tex]First, we will subtract 17 to both sides:
[tex]\begin{gathered} x^2+12x+25-17=17-17 \\ x^2+12x+8=0 \end{gathered}[/tex]We get an expression of the form:
[tex]ax^2+bx+c=0[/tex]To complete the square we will add and subtract the following term:
[tex]\frac{b^2}{4a}[/tex]Replacing the values:
[tex]\frac{12^2}{4(1)}=36[/tex]Therefore, we will add and subtract 36:
[tex]x^2+12x+36-36+8=0[/tex]Now we associate the first three terms:
[tex](x^2+12x+36)-36+8=0[/tex]Now we factor in the associated terms:
[tex](x+6)^2-36+8=0[/tex]Solving the operations:
[tex](x+6)^2-28=0[/tex]Now we solve for "x", first by adding 28 to both sides:
[tex](x+6)^2=28[/tex]Now we take square root to both sides:
[tex](x+6)=\sqrt[]{28}[/tex]Now we subtract 6 to both sides:
[tex]x=-6\pm\sqrt[]{28}[/tex]Now we factor 28 as 7*4:
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