What are the solutions of x squared + 6 x minus 6 = 10?
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To solve the quadratic equation \( x^2 + 6x - 6 = 10 \), let's go through the steps:

### Step 1: Rearrange the equation
Move 10 to the left-hand side of the equation:

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

Simplify:

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

### Step 2: Use the quadratic formula
The quadratic formula is:

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

In this equation, \(a = 1\), \(b = 6\), and \(c = -16\). Now, substitute these values into the quadratic formula:

\[
x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-16)}}{2(1)}
\]

Simplify the expression under the square root:

\[
x = \frac{-6 \pm \sqrt{36 + 64}}{2}
\]
\[
x = \frac{-6 \pm \sqrt{100}}{2}
\]
\[
x = \frac{-6 \pm 10}{2}
\]

### Step 3: Solve for the two possible values of \(x\)

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 \(x = 2\) and \(x = -8\).

Would you like more details on this? Here are some related questions:

1. What is the discriminant and how does it help in solving quadratics?
2. Can you solve quadratic equations by factoring instead of using the formula?
3. How does completing the square compare to the quadratic formula for solving quadratics?
4. What is the geometric interpretation of solving a quadratic equation?
5. How can we apply quadratic equations to real-world problems?

**Tip**: Always check your solutions by substituting them back into the original equation to verify if they satisfy it.

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

Learn how to solve the quadratic equation x² + 6x - 16 = 0 step-by-step using the quadratic formula. This solution involves key algebraic concepts, including discriminants and the quadratic formula, suitable for students in Grades 8-10.

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