What are the solutions of x squared + 6 x minus 6 = 10?
mc029-2.jpg or mc029-3.jpg
mc029-4.jpg or mc029-5.jpg
mc029-6.jpg or mc029-7.jpg
mc029-8.jpg or mc029-9.jpg

We are given the equation:

\[
x^2 + 6x - 6 = 10
\]

### Step 1: Rearrange the equation
Move 10 to the left side to set the equation to zero:

\[
x^2 + 6x - 6 - 10 = 0
\]
\[
x^2 + 6x - 16 = 0
\]

### Step 2: Solve using the quadratic formula
For any quadratic equation \( ax^2 + bx + c = 0 \), the solutions are given by the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 1 \), \( b = 6 \), and \( c = -16 \). Plug these values into the formula:

\[
x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-16)}}{2(1)}
\]
\[
x = \frac{-6 \pm \sqrt{36 + 64}}{2}
\]
\[
x = \frac{-6 \pm \sqrt{100}}{2}
\]
\[
x = \frac{-6 \pm 10}{2}
\]

### Step 3: Find the two solutions
1. \( x_1 = \frac{-6 + 10}{2} = \frac{4}{2} = 2 \)
2. \( x_2 = \frac{-6 - 10}{2} = \frac{-16}{2} = -8 \)

### Final solutions:
The solutions are:
\[
x = 2 \quad \text{or} \quad x = -8
\]

Would you like further details on how this was solved, or have any other questions?

---

Here are 5 related questions you might want to explore:
1. How do you complete the square for the equation \( x^2 + 6x - 16 = 0 \)?
2. Can you factorize the quadratic expression \( x^2 + 6x - 16 \)?
3. What happens if the discriminant in the quadratic formula is negative?
4. How would you graph the quadratic function \( x^2 + 6x - 16 \)?
5. What are the roots of a general quadratic equation?

**Tip:** Always check the discriminant \( b^2 - 4ac \) to determine whether the quadratic has real, complex, or repeated solutions.

What are the solutions of x squared + 6x - 6 = 10?

Discover the step-by-step solution for the quadratic equation x² + 6x - 6 = 10. This guide covers key algebraic concepts, the quadratic formula, and how to calculate the discriminant. Ideal for students in Grades 9-10 looking to master solving quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation