Math Problem Statement

Solve the question in the image without showing the working out

(x - 3)^2 + 2x = 11. Give your solutions correct to 2 decimal places.

Solution

The solutions to the equation are:

x=0.45orx=4.45x = -0.45 \quad \text{or} \quad x = 4.45

Would you like more details or have any questions?

Here are five related questions for further exploration:

  1. How do you solve quadratic equations in general?
  2. What are the different methods for solving quadratic equations?
  3. How do you graph quadratic equations, and what do their solutions represent on the graph?
  4. What is the discriminant, and how does it affect the nature of the solutions?
  5. Can all quadratic equations be solved using factoring?

Tip: Always check your solutions by substituting them back into the original equation to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations

Formulas

Quadratic equation: ax^2 + bx + c = 0
Factoring
Completing the square

Theorems

Quadratic Formula
Completing the Square Method

Suitable Grade Level

Grades 9-10