Which equation has the same solution as x, squared, minus, 20, x, minus, 9, equals, 6x 
2
 −20x−9=6

Let's begin by solving the equation \( x^2 - 20x - 9 = 6 \). 

### Step 1: Move all terms to one side.
Subtract \( 6 \) from both sides to set the equation to zero:
\[
x^2 - 20x - 9 - 6 = 0
\]
\[
x^2 - 20x - 15 = 0
\]

### Step 2: Check the type of equation.
This is a quadratic equation of the form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \)
- \( b = -20 \)
- \( c = -15 \)

### Step 3: Solve using the quadratic formula.
The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute the values of \( a \), \( b \), and \( c \) into the formula:
\[
x = \frac{-(-20) \pm \sqrt{(-20)^2 - 4(1)(-15)}}{2(1)}
\]
\[
x = \frac{20 \pm \sqrt{400 + 60}}{2}
\]
\[
x = \frac{20 \pm \sqrt{460}}{2}
\]
\[
x = \frac{20 \pm \sqrt{460}}{2}
\]

Thus, the solutions are:
\[
x = \frac{20 + \sqrt{460}}{2} \quad \text{or} \quad x = \frac{20 - \sqrt{460}}{2}
\]

These are the solutions to the given equation.

Would you like further details on solving this quadratic or have any other questions?

### 5 Related Questions:
1. How do you factor a quadratic equation instead of using the quadratic formula?
2. What are some common methods for solving quadratic equations?
3. Can all quadratic equations be solved using factoring?
4. How do you approximate the square root of non-perfect squares like \( \sqrt{460} \)?
5. What are some real-world applications of solving quadratic equations?

**Tip:** Always check if a quadratic can be factored first—it can save time over using the quadratic formula!

Which equation has the same solution as x squared minus 20x minus 9 equals 6?

Learn how to solve the quadratic equation x² - 20x - 9 = 6 with step-by-step instructions. This problem covers key algebraic concepts, such as using the quadratic formula to find solutions. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation