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24x²+6x+46=0 solve for x

Sagot :

mathstudent55

Answer:

[tex] x = -\dfrac{1}{8} + \dfrac{\sqrt{1095}}{24}i [/tex]  or  [tex] x = -\dfrac{1}{8} - \dfrac{\sqrt{1095}}{24}i [/tex]

Step-by-step explanation:

24x² + 6x + 46 = 0

Divide both sides by t he GCF, 2:

12x² + 3x + 23 = 0

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

We have a = 12; b = 3; c = 23.

[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(12)(23)}}{2(12)} [/tex]

[tex] x = \dfrac{-3 \pm \sqrt{9 - 1104}}{24} [/tex]

[tex] x = \dfrac{-3 \pm \sqrt{-1095}}{24} [/tex]

[tex] x = \dfrac{-3 \pm i\sqrt{1095}}{24} [/tex]

[tex] x = -\dfrac{1}{8} + \dfrac{\sqrt{1095}}{24}i [/tex]  or  [tex] x = -\dfrac{1}{8} - \dfrac{\sqrt{1095}}{24}i [/tex]

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