Question

(x – 13)2 = 13(x – 13);​

Answer 1

Объяснение:

$(x-13)^2=13*(x-13)\\(x-13)^2-13*(x-13)=0\\(x-13)(x-13-13)=0\\(x-13)(x-26)=0\\x-13=0\ \ \ \ x-26=0\\x_1=13\ \ \ \ \ \ \ \ x_2=26.$

Answer 2

To solve the given equation, you can follow these steps:

Step 1: Expand both sides of the equation:

Expand the left side: (x - 13)^2 = x^2 - 26x + 169

Expand the right side: 13(x - 13) = 13x - 169

So, the equation becomes: x^2 - 26x + 169 = 13x - 169

Step 2: Move all terms to one side of the equation: x^2 - 26x + 169 - 13x + 169 = 0

Simplify the terms: x^2 - 39x + 338 = 0

Step 3: Factor or use the quadratic formula to solve for x:

Since the equation doesn't seem to easily factor, you can use the quadratic formula to solve for x: x = (-b ± √(b^2 - 4ac)) / 2a

In the equation x^2 - 39x + 338 = 0: a = 1, b = -39, c = 338

Calculate the discriminant (b^2 - 4ac): Discriminant = (-39)^2 - 4 * 1 * 338 = 1521 - 1352 = 169

Since the discriminant is positive, there are two real solutions: x = (-(-39) ± √169) / (2 * 1) x = (39 ± 13) / 2

So, the solutions are: x = (39 + 13) / 2 = 26 x = (39 - 13) / 2 = 13

Therefore, the solutions for the equation (x - 13)^2 = 13(x - 13) are x = 26 and x = 13.