Question

(x+15)^2=60x Решить уравнение, помогите, обьясните пожалуйста)

Answer 1

(х+15)² = 60х
х² + 30х +225 - 60х = 0
х² - 30х +225 = 0
(х -15)² =0
х = 15
или Д = 900- 4*225=0
х = 30/2 =15
 

Answer 2

Solving the Equation (x+15)^2 = 60x

To solve the equation (x+15)^2 = 60x, we can follow these steps:

Step 1: Expand the equation by squaring the binomial (x+15): (x+15)(x+15) = 60x

Step 2: Simplify the equation: x^2 + 30x + 225 = 60x

Step 3: Move all terms to one side of the equation: x^2 + 30x - 60x + 225 = 0

Step 4: Combine like terms: x^2 - 30x + 225 = 0

Now we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -30, and c = 225. We can solve this equation using factoring, completing the square, or the quadratic formula.

Using Factoring to Solve the Equation

Step 1: Factor the quadratic equation: (x - 15)(x - 15) = 0

Step 2: Set each factor equal to zero: x - 15 = 0 or x - 15 = 0

Step 3: Solve for x: x = 15 or x = 15

Therefore, the solution to the equation (x+15)^2 = 60x is x = 15.

Verification of the Solution

To verify the solution, we can substitute x = 15 back into the original equation and check if both sides are equal.

Substituting x = 15 into the equation (x+15)^2 = 60x: (15+15)^2 = 60(15) 30^2 = 900

The left side of the equation is equal to the right side, so the solution x = 15 is verified.

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