Solve (x-4)² = (x+2)(x-1): Perfect Square Equals Product

Question

(x4)2=(x+2)(x1) (x-4)^2=(x+2)(x-1)

Video Solution

Solution Steps

00:00 Find X
00:04 We'll use shortened multiplication formulas to open the brackets
00:08 Open brackets properly, multiply each factor by each term
00:33 Simplify what we can
00:42 Isolate X
00:57 And this is the solution to the question

Step-by-Step Solution

To solve the equation (x4)2=(x+2)(x1)(x-4)^2 = (x+2)(x-1), follow these detailed steps:

  • Step 1: Expand the left side of the equation using the square of a binomial formula: (x4)2=x28x+16(x-4)^2 = x^2 - 8x + 16.
  • Step 2: Expand the right side using the distributive property: (x+2)(x1)=x(x1)+2(x1)=x2x+2x2=x2+x2(x+2)(x-1) = x(x-1) + 2(x-1) = x^2 - x + 2x - 2 = x^2 + x - 2.
  • Step 3: Set the expanded forms equal to each other: x28x+16=x2+x2x^2 - 8x + 16 = x^2 + x - 2.
  • Step 4: Subtract x2x^2 from both sides to simplify: 8x+16=x2-8x + 16 = x - 2.
  • Step 5: Move all terms involving xx to one side and constant terms to the other: 8xx=216-8x - x = -2 - 16.
  • Step 6: Combine like terms: 9x=18-9x = -18.
  • Step 7: Solve for xx by dividing both sides by 9-9: x=2x = 2.

Therefore, the solution to the problem is x=2x = 2.

Answer

x=2 x=2