Solve the Equation: (x-1)² = x² | Comparing Perfect Squares

Solve the following equation:

(x1)2=x2 (x-1)^2=x^2

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's use the shortened multiplication formulas to expand the brackets
00:10 Calculate the multiplications and the square
00:17 Simplify what we can
00:24 Isolate X
00:35 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Solve the following equation:

(x1)2=x2 (x-1)^2=x^2

2

Step-by-step solution

Let's examine the given equation:

(x1)2=x2 (x-1)^2=x^2 First, let's simplify the equation, using the perfect square binomial formula:

(a±b)2=a2±2ab+b2 (a\pm b)^2=a^2\pm2ab+b^2 ,

We'll start by opening the parentheses on the left side using the perfect square formula and then move terms and combine like terms, in the final step we'll solve the resulting simplified equation:

(x1)2=x2x22x1+12=x2x22x+1=x22x=1/:(2)x=12 (x-1)^2=x^2 \\ \downarrow\\ x^2-2\cdot x\cdot1+1^2=x^2\\ x^2-2x+1= x^2\\ -2x=-1\hspace{6pt}\text{/}:(-2)\\ \boxed{x=\frac{1}{2}} Therefore, the correct answer is answer A.

3

Final Answer

x=12 x=\frac{1}{2}

Practice Quiz

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Solve the following equation:


\( 2x^2-8=x^2+4 \)

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