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Solve x2 + 12x = –20 by completing the square. Add to both sides of the equation. The value of in this equation is . Write the left side of the equation as a binomial squared. The left side of the equation becomes ()2. Use the square root property of equality. Isolate the variable: x =

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Answer:

(36) (x+6) (-10 or -2) i got this right on (ed)

Step-by-step explanation:

1 Add  to both sides of the equation. The value of  in this equation is 36.

2 Write the left side of the equation as a binomial squared. The left side of the equation becomes (x +6)2.

3 Use the square root property of equality.

4 Isolate the variable: x = -10 or -2

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The solutions of [tex]x^{2}+12\cdot x = -20[/tex] are [tex]x_{1} = -10[/tex] and [tex]x_{2} = -2[/tex].

How to factor the second order polynomial by completing the square

In this question we must simplify the second order polynomial by algebraic means and then obtain the roots of the polynomial:

  1. [tex]x^{2}+12\cdot x = -20[/tex]     Given
  2. [tex]x^{2}+12\cdot x +36 = -20 + 36[/tex]   Compatibility with addition
  3. [tex]x^{2}+12\cdot x + 36 = 16[/tex]   Definition of addition/Existence of additive inverse/Modulative property
  4. [tex](x+6)^{2} = 16[/tex]    Perfect square trinomial
  5. [tex]x+6 = \pm 4[/tex] Definition of square root
  6. [tex]x = -6 \pm 4[/tex]  Compatibility with addition/Definition of addition/Existence of additive inverse/Modulative property/Result

The solutions of [tex]x^{2}+12\cdot x = -20[/tex] are [tex]x_{1} = -10[/tex] and [tex]x_{2} = -2[/tex]. [tex]\blacksquare[/tex]

To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016