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Verified Answer :

SociometricStar

Answer:

x = -10, -2

Step-by-step explanation:

The given equation is \(x^2+12x=-20\)

We can rewrite this equation by adding 20 to both sides as

\(x^2+12x+20=0\)

Comparing with \(ax^2+bx+c=0\), we get

a=1

b = 12

c = 20

Now, add \((\frac{b}{2})^2\) to both sides of the equation.

\((\frac{b}{2})^2\\\\=(12/2)^2\\\\=6^2=36\)

So add 36 to both sides of the equation

\(x^2+12x+36+20=36\)

Subtract 20 to both sides

\(x^2+12x+36=16\)

We can rewrite the left hand side of the equation as

\((x+6)^2=16\)

Take square root both sides

\(\sqrt{(x+6)^2}=\pm\sqrt{16}\\\\x+6=\pm4\\\\x=4-6,-4-6\\\\x=-2,-10\)

Thus, the values of x are x = -10, -2

Correct response:

The solution of the equation are; x = -2 or x = -10

Details of the completing the square method used

The given quadratic equation is; x² + 12·x = -20

Required:

To solve the quadratic equation by completing the square

Solution:

The equation is presented in the form; x² + b·x = c

By completing the square, we have;

  • \(\mathbf{x^2 + b \cdot x + \left(\dfrac{b}{2} \right)^2} = c + \left( \dfrac{b}{2} \right)^2\)

Comparison with the given equation gives;

\(\mathbf{x^2 + 12 \cdot x + \left(\dfrac{12}{2} \right)^2} = -20 + \left(\dfrac{12}{2} \right)^2\)

x² + 12·x + 6² = -20 + 6² = 16 = 4²

Therefore, we have;

x² + 12·x + 6² = (x + 6)² = 4²

x + 6 = ±4

x = ±4 - 6

  • x = -2, or x = -10

Verification gives;

(x + 2) × (x + 10) = x² + 12·x + 20 = 0

Which gives;

x² + 12·x = -20 (the given equation)

Therefore;

The solutions of the equation x² + 12·x = -20 found by completing the square, are;

x = -2, or x = -10

Learn more about completing the square method here:

https://brainly.com/question/3939104