Question

Solve x2 + 12x + 8 = 0 by completing the square. Identify all of the possible solutions.

Answer 1

Answer:

$x=-6+2\sqrt{7}$

$x=-6-2\sqrt{7}$

Step-by-step explanation:

Completing the square

when  $ax^2+bx+c=0$

Given equation:

$x^2+12x+8=0$

Subtract 8 from both sides:

$\implies x^2+12x=-8$

Add the square of half the coefficient of $x$ to both sides:

$(\frac{b}{2})^2=(\frac{12}{2})^2=36$

$\implies x^2+12x+36=-8+36$

Factor the left side and simplify the right side:

$\implies (x+6)^2=28$

Subtract 28 from both sides:

$\implies (x+6)^2-28=0$

Solve

$\implies (x+6)^2=28$

$\implies x+6=\pm\sqrt{28}$

$\implies x+6=\pm\sqrt{4 \cdot 7}$

$\implies x+6=\pm\sqrt{4}\sqrt{7}$

$\implies x+6=\pm2\sqrt{7}$

$\implies x=-6\pm2\sqrt{7}$

Answer 2

• x²+12x+8=0
• x²+12x=-8

Multiply 4a

• 4(x²+12x)=-32
• 4x²+48x=-32
• (2x)²+2(2x)(12)=-32

Add b²

• (2x)²+2(2x)(12)+12²=12²-32
• (2x+12)²=144-32
• (2x+12)²=112
• 2x+12=±√112
• 2(x+6)=2√28
• x+6=±√28
• x=-6±2√7