Solve for x in the equation (x − 7)^2 − 4 = (x + 1)^2.

(x − 7)^2 − 4 = (x + 1)^2

x^2 - 14x + 49 - 4 = x^2 + 2x + 1
-16x = -44
x = 44/16 = 11/4 or 2.75

follow up quesiton

11/4 or 2.75

how do u convert this without using calculator?

to divide by 4 in my head,

I take half of my number and then I take another half

(little tricks that old people still know and use)

so half of 11 is 5.5 and half of 5.5 is 2.75
Think of money, half of $5.50
half of $5 is 2.50, and half of 50 cents is 25 cents
what is 2.50 + 25 cents ?

To solve for x in the equation, you can follow these steps:

Step 1: Expand the squared terms on both sides of the equation.
(x − 7)(x − 7) − 4 = (x + 1)(x + 1)

Step 2: Simplify the expanded expressions.
(x^2 − 14x + 49) − 4 = (x^2 + 2x + 1)

Step 3: Remove the parentheses and reorganize the equation.
x^2 − 14x + 49 − 4 = x^2 + 2x + 1

Step 4: Combine like terms.
x^2 − 14x + 45 = x^2 + 2x + 1

Step 5: Subtract x^2 from both sides of the equation to eliminate the x^2 terms.
−14x + 45 = 2x + 1

Step 6: Move the variable terms to one side and the constant terms to the other side.
−14x − 2x = 1 − 45

Step 7: Combine like terms and simplify.
−16x = -44

Step 8: Divide both sides of the equation by -16 to solve for x.
x = -44 / -16

Step 9: Simplify the division.
x = 11/4 or x = 2.75

Therefore, the solution for x in the equation (x − 7)^2 − 4 = (x + 1)^2 is x = 11/4 or x = 2.75.