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{$\begin{gathered}\sf \boldsymbolx_(1)=(-b-√(\Delta) )/(2a ) \end{gathered}$}`

The end solution:

`\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{√(\Delta)=√(228)=√(4*57)=√(4)*√(57)=2√(57) } \end{gathered}$}`

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

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

{ Pisces04 }