Solve (x+1)² = x² : Perfect Square Equation Challenge

Question

Solve the following equation:

(x+1)2=x2 (x+1)^2=x^2

Video Solution

Solution Steps

00:00 Solve
00:03 Let's use shortened multiplication formulas to open the parentheses
00:10 Calculate the multiplication and the square
00:16 Simplify what we can
00:23 Isolate X
00:32 And this is the solution to the question

Step-by-Step Solution

Let's examine the given equation:

(x+1)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 simplified equation we get:

(x+1)2=x2↓x2+2⋅x⋅1+12=x2x2+2x+1=x22x=−1/:2x=−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.

Answer

x=−12 x=-\frac{1}{2}

More Questions

Related Subjects

The formula for the sum of squares Abbreviated Multiplication Formulas

Question Types

Square of sum: Using short multiplication formulas Square of sum: Solving the problem