Question

By completing the square method 2x2-15x+25

Answer 1

Answer:

Solving 2x2-15x+25 = 0 by Completing The Square .

Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :

x2-(15/2)x+(25/2) = 0

Subtract 25/2 from both side of the equation :

x2-(15/2)x = -25/2

Now the clever bit: Take the coefficient of x , which is 15/2 , divide by two, giving 15/4 , and finally square it giving 225/16

Add 225/16 to both sides of the equation :

On the right hand side we have :

-25/2 + 225/16 The common denominator of the two fractions is 16 Adding (-200/16)+(225/16) gives 25/16

So adding to both sides we finally get :

x2-(15/2)x+(225/16) = 25/16

Adding 225/16 has completed the left hand side into a perfect square :

x2-(15/2)x+(225/16) =

(x-(15/4)) • (x-(15/4)) =

(x-(15/4))2

Things which are equal to the same thing are also equal to one another. Since

x2-(15/2)x+(225/16) = 25/16 and

x2-(15/2)x+(225/16) = (x-(15/4))2

then, according to the law of transitivity,

(x-(15/4))2 = 25/16

We'll refer to this Equation as Eq. #4.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(15/4))2 is

(x-(15/4))2/2 =

(x-(15/4))1 =

x-(15/4)

Now, applying the Square Root Principle to Eq. #4.2.1 we get:

x-(15/4) = √ 25/16

Add 15/4 to both sides to obtain:

x = 15/4 + √ 25/16

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Since a square root has two values, one positive and the other negative

x2 - (15/2)x + (25/2) = 0

has two solutions:

x = 15/4 + √ 25/16

or

x = 15/4 - √ 25/16

Note that √ 25/16 can be written as

√ 25 / √ 16 which is 5 / 4

Answer 2

Step-by-step explanation:

$2 {x}^{2} - 15x + 25 = 0$

$\div 2→ {x}^{2} - \frac{15}{2} x + \frac{25}{2} = 0$

${x}^{2} - \frac{15}{2} = \frac{ - 25}{2}$

${x }^{2} - (\frac{2}{2})( \frac{15}{2})x = - \frac{25}{2}$

${x }^{2} - 2 (\frac{15}{4} )x = - \frac{25}{2}$

${x}^{2} - 2 (\frac{15}{4} )x + \frac{225}{16} = \frac{225}{16} - \frac{25}{2}$

$( {x - \frac{15}{4} )}^{2} = \frac{25}{16}$

$x - \frac{15}{4} = ± \sqrt{ \frac{25}{16} }$

$x - \frac{15}{4} = ± \frac{5}{4}$

$x = \frac{15}{4} - \frac{5}{4} ;x = \frac{15}{4} + \frac{5}{4}$

$x = \frac{10}{4} ;x = \frac{20}{4}$

$x = \frac{5}{2} ;x = 5$

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