To solve the equation 5x^2 = 2x + 10 + 4, we need to isolate the variable x.
1. First, let's simplify the right side of the equation:
- 2x + 10 + 4 = 2x + 14
2. Now, our equation becomes 5x^2 = 2x + 14.
3. Next, we'll move all terms to one side of the equation to set it equal to zero:
- 5x^2 - 2x - 14 = 0
4. This is now a quadratic equation. We can try to factor it or use the quadratic formula to find the values of x. Let's use the quadratic formula:
- x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 5, b = -2, and c = -14.
5. Plugging in the values, we get:
- x = (-(-2) ± √((-2)^2 - 4 * 5 * -14)) / (2 * 5)
- x = (2 ± √(4 + 280)) / 10
- x = (2 ± √284) / 10
6. Simplifying further, we have:
- x = (2 ± 2√71) / 10
- x = (1 ± √71) / 5
Therefore, the solutions to the equation 5x^2 = 2x + 10 + 4 are x = (1 + √71) / 5 and x = (1 - √71) / 5.