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Directions and Analysis
Task 1: Completing the Square
Look at the quadratic equation below.
2x^2-12x-16=0



This is not an equation that could be easily solved by factoring. Instead, you are going to use the method of completing the square to solve this equation. Follow each step in this task to complete the square and solve the equation.

a. To complete the square, the coefficient of the x2 term must be 1. Divide both sides of the equation by a value and rewrite the equation to meet this criteria.

Type your response here:


b. Rewrite the resulting equation so the constant term is on the right side of the equation and the variable terms are on the left.

Type your response here:


c. Identify the coefficient of the x term in the previous equation. Then divide it by half and square the result. What is the result?

Type your response here:


d. Add the value you identified in part c to both sides of the equation from part b and simplify the right side. Remember that when solving equations, whatever is done to one side of the equation must also be done to the other side the equation: that is why you must add the value to both sides.

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e. Notice that the left side of the equation now represents a perfect square quadratic expression. Use this fact to rewrite the left side of the previous equation as the square of a linear term and create a new equation.

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f. You have now completed the square. Starting with the result from part e, solve the equation for x. Show your work.

Type your response here:


g. Now that you know how to complete the square to solve a quadratic equation, solve the equation 3x^2 – 3x − 6 = 0. Show your work.

Type your response here:

Respuesta :

Answer:

a. [tex]x^2-6x-8=0[/tex]

b. [tex]x^2-6x=8[/tex]

c.

[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]

Also, [tex](-3)^2=9[/tex]

d. [tex]x^2-6x+9=17[/tex]

e. [tex](x-3)^2=17[/tex]

f, g. [tex]x=3\pm \sqrt{17}[/tex]

Step-by-step explanation:

Given: [tex]2x^2-12x-16=0[/tex]

To solve: the given equation

Solution:

a.

[tex]2x^2-12x-16=0[/tex]

Coefficient of [tex]x^2=2[/tex]

Divide both sides by 2

[tex]x^2-6x-8=0[/tex]

b.

[tex]x^2-6x=8[/tex]

c.

Coefficient of x = -6

[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]

Also, [tex](-3)^2=9[/tex]

d.

Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]

[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]

e.

[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]

f.

[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]

g.

[tex]x=3\pm \sqrt{17}[/tex]

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