Solve (x-4)² + x(x-12) = 16: Finding Parameter x

Find the value of the parameter x.

(x−4)2+x(x−12)=16 (x-4)^2+x(x-12)=16

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Open parentheses according to the shortened multiplication formulas
00:08 Open parentheses properly, multiply by each factor
00:15 Calculate the multiplications and collect terms
00:23 Simplify what's possible
00:34 Factor out common terms
00:43 Find when each factor in the multiplication equals zero
00:47 This is one solution, find the second solution using the same method
00:54 And this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

Find the value of the parameter x.

(x−4)2+x(x−12)=16 (x-4)^2+x(x-12)=16

2

Step-by-step solution

Let's open the parentheses, remembering that there might be more than one solution for the value of X:

(x−4)2+x(x−12)=16 (x-4)^2+x(x-12)=16

x2−8x+16+x2−12x=16 x^2-8x+16+x^2-12x=16

2x2−20x=0 2x^2-20x=0

2x(x−10)=0 2x(x-10)=0

Therefore:

x−10=0 x-10=0

x=10 x=10

Or:

2x=0 2x=0

x=0 x=0

3

Final Answer

x=0,x=10 x=0,x=10

Practice Quiz

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Find the value of the parameter x.

\( 2x^2-7x+5=0 \)

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