Question

(х+1)^2+(х-6)^2=2х^2

Answer 1

$x^{2}+2x + 1+x^{2} -12x+36=2x^{2} \\2x^{2} -2x^{2} -10x+37=0\\10x=37\\x=\frac{37}{10} =3,7\\x=3,7$

Answer 2

Let's solve the given equation:

(х+1)^2 + (х-6)^2 = 2х^2

Step 1: Expand the expressions inside the parentheses.

(х+1)^2 = (х+1)(х+1) = х^2 + 2х + 1

(х-6)^2 = (х-6)(х-6) = х^2 - 12х + 36

Step 2: Substitute the expanded expressions back into the original equation.

(х^2 + 2х + 1) + (х^2 - 12х + 36) = 2х^2

Step 3: Combine like terms.

2х^2 + 2х - 12х + 1 + 36 = 2х^2

Step 4: Simplify.

2х^2 - 10х + 37 = 2х^2

Step 5: Move all terms to one side of the equation.

2х^2 - 2х^2 - 10х + 37 = 0

Step 6: Combine like terms again.

-10х + 37 = 0

Step 7: Move the constant term to the other side of the equation.

-10х = -37

Step 8: Solve for х.

х = -37 / -10

х = 3.7

So, the solution to the equation is х = 3.7.