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Algebra - Completing the Square

by James
(Kentucky)











































16x^-64x=0
Please answer by completing the square, and show your work thanks

Comments for Algebra - Completing the Square

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Jan 26, 2012
Completing the Square
by: Staff

Question:

by James
(Kentucky)


16x^-64x=0

Please answer by completing the square, and show your work thanks


Answer:

16x² - 64x = 0

You can solve for x by completing the square (shown below). However, the easiest way to solve this problem is by factoring the expression on the left side of the equal sign.


Solving by factoring:

16x² - 64x = 0

16(x² - 4x) = 0

16x(x - 4) = 0

x = 0

x = 4

x ∈ {0, 4}


Solve by completing the square:

To complete the square, begin by writing the quadratic equation in this format:

ax² + bx + c = 0


(a) 16x² - 64x + 0 = 0

To reduce the size of the numbers, divide each side of the equation by 16

16x² - 64x + 0 = 0

(16x² - 64x + 0)/16 = 0/16

x² - 4x + 0 = 0


a = 1

b = -4

c = 0


subtract c from each side of the equation to move the c to the right side of the equation (since c = 0, this step is not necessary. I am merely showing the entire process of completing the square)

x² - 4x + 0 - 0 = 0 - 0

x² - 4x + 0 = 0




Divide the coefficient b (which is -4) by 2

- 4/2 = -2

Square the result

(-2)² = 4

Add this value to each side of the equation. This means that you will add 4 to each side of the equation.
x² - 4x + 4 = 0 + 4

x² - 4x + 4 = 4

THE REASON for adding the 2 to each the right side of the equation is: CHANGE THE LEFT SIDE OF THE EQUATION SO IT CAN BE FACTORED AS A PERFECT SQUARE:

x² - 4x + 4 = 4

(x - 2)² = 4

Take the square root of each side of the equation

√(x - 2)² = ±√(4)

x - 2 = ±√(4)


Add 2 from each side of the equation to remove the 2 from the left side of the equation. This leaves the variable x as the only term on the left side of the equation.

x - 2 + 2 = +2 ±√(4

x + 0 = 2 ±√(4)

x = 2 ±√(4)


1st value of x₁ = 2 plus the square root of 4

x₁ = 2 + √(4)

x₁ = 2 + 2

x₁ = 4


2nd value of x₂ = 2 minus the square root of 4

x₂ = 2 - √(4)

x₂ = 2 - 2


x₂ = 0



x ∈{0, 4}


the final answer to part (a) is:

x = 2 ±√(4)

or

x ∈{0, 4}



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check the solution by substituting the two numerical values of x into the original equation


for x₁ = 4

16x² - 64x = 0


16*(4)² - 64(4) = 0

256 - 256 = 0

0 = 0, OK → x₁ = 4 is a valid solution


for x₂ = 0

16x² - 64x = 0

16*(0)² - 64*(0) = 0

0 - 0 = 0

0 = 0, OK → x₂ = 0 is a valid solution




Thanks for writing.
Staff

www.solving-math-problems.com


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