Question

4x² + 6x = 12
Solve by completing square​

Answer 1

4x² + 6x = 12

We move all the terms to the left:

• a = 4; b = 6; c = -12;
• Δ = b² - 4ac
• Δ = 6² - 4 · 4 · ( -12 )
• Δ = 228

The value of Δ is greater than zero, so the equation has two solutions

We use the following formulas to compute our solutions:

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a }| \ x_{2}=\dfrac{-b+\sqrt{\Delta} }{2a } } \end{gathered} }$

The end solution:

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57} } \end{gathered} }$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a}=\dfrac{-(6)-2\sqrt{57} }{2*4}=\dfrac{-6-2\sqrt{57} }{8} } \end{gathered} }$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b+\sqrt{\Delta} }{2a}=\dfrac{-(6)+2\sqrt{57} }{2*4}=\dfrac{-6+2\sqrt{57} }{8} } \end{gathered} }$

{ Pisces04 }