Questions: Solve the equation by the method of your choice. x^2 + 4x = 10 The solution set is □ (Simplify your answer, including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Solve the equation by the method of your choice. x^2 + 4x = 10 The solution set is □ (Simplify your answer, including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Transcript text: Solve the equation by the method of your choice. \[ x^{2}+4 x=10 \] The solution set is $\square$ (Simplify your answer, including any radicals and $i$ as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
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Solution

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Solution Steps

Step 1: Set Up the Equation

We start with the quadratic equation: \[ x^{2} + 4x - 10 = 0 \]

Step 2: Solve for \( x \)

Using the quadratic formula or factoring, we find the solutions: \[ x = -2 + \sqrt{14} \quad \text{and} \quad x = -2 - \sqrt{14} \]

Step 3: Simplify the Solutions

The solutions can be expressed as: \[ x_1 = -2 + \sqrt{14}, \quad x_2 = -2 - \sqrt{14} \]

Final Answer

The solution set is: \[ \boxed{-2 + \sqrt{14}, -2 - \sqrt{14}} \]

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