Question

Write an equation to find (x) if the total area of the model is 110 m². Solve the equation by completing the square.

Answer 1

The equation to find x for the total area of the model, given as 110 m², using the method of completing the square is (x - 5)² = 35. Solving this equation will yield the value of x.

Explanation:

To derive the equation (x - 5)² = 35, consider the formula for the area of a square, A = side². Let x be the side length of the square representing the model.

The total area is given as 110 m², so x² = 110. To complete the square, subtract the constant term on both sides, x² - 110 = 0. To create a perfect square trinomial, add half of the coefficient of x squared to both sides, resulting in x² - 10x + 25 = 35. Simplify to (x - 5)² = 35, the completed square form of the equation.

Now, to solve for x, take the square root of both sides: x - 5 = ±√35. Add 5 to both sides to isolate x, giving x = 5 ± √35. Thus, the solution to the equation is x = 5 + √35 or x = 5 - √35, representing the possible side lengths of the square model

Answer 2

The question pertains to solving a quadratic equation using the method of completing the square. The response provides a simplified explanation and a sample process for solving such equations.

Step-by-step explanation:

The question involves solving a quadratic equation by completing the square to find the value of x. Although the provided statements do not clearly present an equation related to the area, a general approach to solve a quadratic equation by completing the square involves rearranging the equation into the form x² + bx + c = 0, then rewriting it as (x + b/2)² = (b/2)² - c, after which one can take the square root of both sides and solve for x.

Here is an example using a generic quadratic equation: Suppose we have x² + 6x - 16 = 0. We can complete the square by adding (6/2)², which is 9, to both sides to get x² + 6x + 9 = 25. This simplifies to (x + 3)² = 25, and from here, we take the square root of both sides and obtain x = -3 ± 5, giving us two possible solutions, x = 2 or x = -8.