Question

Solve by completing the square

Answer 1

`4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \frac 32 \cdot x+\left(\frac 32 \right)^2 - \left(\frac 32\right)^2 =8\\ \\\implies \left(x+\frac 32 \right)^2 = 8 + \frac 94 = \frac{41}4\\\\\implies x+\frac 32 = \pm\frac{√(41)}2\\\\\implies x = \pm \frac{\sqrt {41}}2 - \frac 32\\\\\text{The roots are}~ x = -\frac 32-\frac{√(41)}2~ \text{and}~~ x = -\frac 32+\frac{√(41)}2`