Let's solve the equation step by step.

Given equation:
\[
2x^2 - 3(x + 2) + 5 = 2(x - 5)^2
\]

### Step 1: Expand the expressions
1. Expand \( -3(x + 2) \):
   \[
   -3(x + 2) = -3x - 6
   \]
2. Expand \( 2(x - 5)^2 \). First, expand \( (x - 5)^2 \):
   \[
   (x - 5)^2 = x^2 - 10x + 25
   \]
   Then, multiply by 2:
   \[
   2(x^2 - 10x + 25) = 2x^2 - 20x + 50
   \]

### Step 2: Substitute the expanded expressions into the equation
\[
2x^2 - 3x - 6 + 5 = 2x^2 - 20x + 50
\]

Simplify the left side:
\[
2x^2 - 3x - 1 = 2x^2 - 20x + 50
\]

### Step 3: Subtract \( 2x^2 \) from both sides to eliminate the quadratic term
\[
-3x - 1 = -20x + 50
\]

### Step 4: Add \( 20x \) to both sides to gather the \( x \)-terms on one side
\[
17x - 1 = 50
\]

### Step 5: Add 1 to both sides
\[
17x = 51
\]

### Step 6: Divide by 17 to solve for \( x \)
\[
x = \frac{51}{17} = 3
\]

So, the solution is \( x = 3 \).

Would you like any details or have any questions about the solution?

---

Here are some related questions:
1. How do you expand binomials using the distributive property?
2. What is the process for simplifying polynomial expressions?
3. Can you solve quadratic equations using different methods?
4. How do you solve systems of linear equations?
5. What is the importance of isolating variables in algebraic equations?

**Tip:** When dealing with equations that involve polynomials, always remember to carefully expand and simplify all expressions before trying to solve for the variable.

Learn how to solve the equation 2x^2 - 3(x + 2) + 5 = 2(x - 5)^2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations, expanding expressions, and simplifying equations. Suitable for high school students and advanced learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation