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Solve x2 + 12x + 8 = 0 by completing the square. Identify all of the possible solutions.
A 6+√7
B. -6+2V7
o c. 6-2V7
D. 6-7
-
O E 6-27

Respuesta :

semsee45

Answer:

[tex]x=-6+2\sqrt{7}[/tex]

[tex]x=-6-2\sqrt{7}[/tex]

Step-by-step explanation:

Completing the square

when  [tex]ax^2+bx+c=0[/tex]

Given equation:

[tex]x^2+12x+8=0[/tex]

Subtract 8 from both sides:

[tex]\implies x^2+12x=-8[/tex]

Add the square of half the coefficient of [tex]x[/tex] to both sides:

[tex](\frac{b}{2})^2=(\frac{12}{2})^2=36[/tex]

[tex]\implies x^2+12x+36=-8+36[/tex]

Factor the left side and simplify the right side:

[tex]\implies (x+6)^2=28[/tex]

Subtract 28 from both sides:

[tex]\implies (x+6)^2-28=0[/tex]

Solve

[tex]\implies (x+6)^2=28[/tex]

[tex]\implies x+6=\pm\sqrt{28}[/tex]

[tex]\implies x+6=\pm\sqrt{4 \cdot 7}[/tex]

[tex]\implies x+6=\pm\sqrt{4}\sqrt{7}[/tex]

[tex]\implies x+6=\pm2\sqrt{7}[/tex]

[tex]\implies x=-6\pm2\sqrt{7}[/tex]
  • 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

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