To solve \( 5x^2 = 6 + 8 \) by completing the square, follow these steps:

### Step 1: Simplify the equation
First, simplify the right-hand side:
\[
5x^2 = 6 + 8 \implies 5x^2 = 14
\]

### Step 2: Divide by the coefficient of \(x^2\)
To make the coefficient of \(x^2\) equal to 1, divide the entire equation by 5:
\[
x^2 = \frac{14}{5}
\]

### Step 3: Complete the square
In this case, since the equation is already in the form \(x^2 = \frac{14}{5}\), we don't need to complete the square further. We can directly solve for \(x\) by taking the square root of both sides.

### Step 4: Solve for \(x\)
\[
x = \pm \sqrt{\frac{14}{5}} = \pm \frac{\sqrt{14}}{\sqrt{5}} = \pm \frac{\sqrt{14}}{5}
\]

Thus, the solutions are:
\[
x = \pm \frac{\sqrt{14}}{5}
\]

Would you like further details or explanations?

### Related Questions:
1. How can completing the square be applied to quadratic equations with a non-zero linear term?
2. Can completing the square be used to solve any quadratic equation?
3. How does completing the square relate to the quadratic formula?
4. What are the advantages of completing the square over factoring?
5. How can the method of completing the square be used to derive the vertex form of a parabola?

**Tip:** Completing the square is useful for converting a quadratic equation into a form that easily reveals the vertex of the parabola.

Discover how to solve the equation 5x² = 6 + 8 by completing the square. This step-by-step guide covers the essential algebraic concepts needed for Grades 9-10, including simplifying, dividing by coefficients, and solving quadratic equations.

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