How do you solve using the completing the square method $x^{2} + 12 x + 23 = 0$ $x^2+12x+23=0$ ?

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How do you solve using the completing the square method $x^{2} + 12 x + 23 = 0$ $x^2+12x+23=0$ ?

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Answer 1 · 2016-03-17T00:05:55

Using the square method we have that

$x^{2} + 12 x + 23 = x^{2} + 2 \cdot 6 \cdot x + 6^{2} + (23 - 6^{2}) = {(x + 6)}^{2} - 13$ $x^2+12x+23=x^2+2*6*x+6^2+(23-6^2)= (x+6)^2-13$

Hence from $x^{2} + 12 x + 23 = 0 \Rightarrow {(x + 6)}^{2} - 13 = 0 \Rightarrow x + 6 = \pm \sqrt{13} \Rightarrow x_{1} = - 6 + \sqrt{13} or x_{2} = - 6 - \sqrt{13}$ $x^2+12x+23=0=>(x+6)^2-13=0=> x+6=+-sqrt13=>x_1=-6+sqrt13 or x_2=-6-sqrt13$

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How do you solve using the completing the square method $x^{2} + 12 x + 23 = 0$ $x^2+12x+23=0$ ?

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