To rewrite the equation \( 2(x^2 + x) = 5 \) in the standard form \( ax^2 + bx + c = 0 \), follow these steps:

### Step 1: Expand and Distribute
Distribute the 2 across the terms inside the parentheses:
\[
2(x^2 + x) = 2x^2 + 2x
\]
So, the equation becomes:
\[
2x^2 + 2x = 5
\]

### Step 2: Move All Terms to One Side
Subtract 5 from both sides to set the equation equal to 0:
\[
2x^2 + 2x - 5 = 0
\]

### Step 3: Identify the Coefficients
Now the equation is in the standard form \( ax^2 + bx + c = 0 \), where:
- \( a = 2 \)
- \( b = 2 \)
- \( c = -5 \)

So, the equation in standard form is:
\[
2x^2 + 2x - 5 = 0
\]

Would you like further details or assistance with a related topic?

### Related Questions
1. How can you solve the quadratic equation \( 2x^2 + 2x - 5 = 0 \)?
2. What are the methods to factorize quadratic equations?
3. How do you calculate the roots of a quadratic equation using the quadratic formula?
4. What is the significance of the discriminant in solving quadratic equations?
5. How do you complete the square for the equation \( 2x^2 + 2x - 5 = 0 \)?
6. How can you graph the quadratic equation \( 2x^2 + 2x - 5 = 0 \)?
7. What are the axis of symmetry and vertex of the quadratic equation?
8. Can you solve a quadratic equation by substitution or elimination methods?

### Tip
When moving all terms to one side, always ensure the quadratic equation is set to zero; this is key for applying various solving methods.

Learn how to solve the quadratic equation 2x^2 + 2x - 5 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation standard form and the quadratic formula theorem. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation