Answer:
x = (-15 + √1017) / 12
x = (-15 - √1017) / 12
Explanation:
To solve for x in the equation 3x(2x + 5) - 23 = 10, follow these steps:
Distribute the 3x on the left side of the equation:
6x^2 + 15x - 23 = 10
Move the constant term (10) to the left side of the equation by subtracting 10 from both sides:
6x^2 + 15x - 23 - 10 = 0
Simplify the equation further:
6x^2 + 15x - 33 = 0
Now, you have a quadratic equation in the form of ax^2 + bx + c = 0. You can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 6, b = 15, and c = -33. Plug these values into the quadratic formula:
x = (-15 ± √(15^2 - 4 * 6 * (-33))) / (2 * 6)
x = (-15 ± √(225 + 792)) / 12
x = (-15 ± √1017) / 12
Now, you have two possible solutions:
x = (-15 + √1017) / 12
x = (-15 - √1017) / 12
These are the solutions for x in the equation. They are not simple integer values but can be expressed as decimal approximations.