Question

x2-15x+54=0 by solve completing square method​

Answer 1

x2−15x+54−54=0−54

x2−15x=−54

Step 2: The coefficient of -15x is -15. Let b=-15.

Then we need to add (b/2)^2=225/4 to both sides to complete the square.

Add 225/4 to both sides.

x2−15x+2254=−54+2254

x2−15x+2254=94

Step 3: Factor left side.

(x−152)2=94

Step 4: Take square root.

x−152=±√94

Step 5: Add 15/2 to both sides.

x−152+152=152±√94

x=152±√94

x=9 or x=6

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Answer 2

The solution is x = 9 or x = 6

Step-by-step explanation:

Given:

equation is x²-15x +54=0

To find:

solve by completing the square method

Solution:

The equation is x²-15x +54=0

It is in the standard form as the coefficient of the first term is 1

here, a= 1, b= -15, c=54

We move c to the right side of the equation

x²-15x = -54

We take b and form the (b/2)² form

here, b= -15

∴ (-15/2)²= 225/4

Adding this to both sides of the equation we get

$x^{2} -15x +\frac{225}{4} = -54 +\frac{225}{4}$

The left side is the form of the identity

$(a-b)^{2}= a^{2}-2ab+b^{2}$

Thus, we add the term (x-15/2)²instead of the identity

∴ $(x-\frac{15}{2} )^{2}= \frac{-54 (4) + 225}{4}$

∴ $(x-\frac{15}{2} )^{2}= \frac{9}{4}$

Now, taking square roots on both sides of the equation we get

∴ $x - \frac{15}{2} = \sqrt{\frac{9}{4} }$

But a square root can have both positive and negative values

∴ $x - \frac{15}{2} = \±\frac{3}{2}$

∴ $x - \frac{15}{2} = \frac{3}{2}\ or\ x - \frac{15}{2} = -\frac{3}{2}$

∴ $x = \frac{3}{2}+\frac{15}{2}\ or\ x = -\frac{3}{2}+\frac{15}{2}$

∴ $x = \frac{18}{2}\ or\ x = \frac{12}{2}$

∴ $x= 9 \ or\ x = 6$

Thus, x = 9 or x= 6 is the solution for the equation  x²-15x +54=0

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