(x−4)2=(x+2)(x−1)
To solve the equation (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: (x−4)2=x2−8x+16.
- Step 2: Expand the right side using the distributive property: (x+2)(x−1)=x(x−1)+2(x−1)=x2−x+2x−2=x2+x−2.
- Step 3: Set the expanded forms equal to each other: x2−8x+16=x2+x−2.
- Step 4: Subtract x2 from both sides to simplify: −8x+16=x−2.
- Step 5: Move all terms involving x to one side and constant terms to the other: −8x−x=−2−16.
- Step 6: Combine like terms: −9x=−18.
- Step 7: Solve for x by dividing both sides by −9: x=2.
Therefore, the solution to the problem is x=2.