Answer: The solutions to the quadratic equation 3x^2 - 15x - 8 = -10x are x = -1/3 and x = 8.
Explanation:
To solve the quadratic equation 3x^2 - 15x - 8 = -10x by factoring, we need to rearrange the equation so that one side is equal to zero.
First, combine like terms on the right side of the equation:
3x^2 - 15x - 8 + 10x = 0
Next, simplify the equation:
3x^2 - 5x - 8 = 0
Now, we need to factor the quadratic expression on the left side of the equation. To do this, we're looking for two binomials in the form (ax + b)(cx + d) that multiply to give us the quadratic expression.
To factor 3x^2 - 5x - 8, we need to find two numbers whose product is -24 (the product of the coefficients of x^2 and the constant term -8) and whose sum is -5 (the coefficient of the x term).
After some trial and error, we find that the numbers -8 and 3 satisfy these conditions.
So, we can rewrite the equation as:
(3x + 1)(x - 8) = 0
Now, we can set each factor equal to zero and solve for x:
3x + 1 = 0 or x - 8 = 0
For the first equation, subtract 1 from both sides and divide by 3:
3x = -1
x = -1/3
For the second equation, add 8 to both sides:
x = 8
Therefore, the solutions to the quadratic equation 3x^2 - 15x - 8 = -10x are x = -1/3 and x = 8.
Hope this helps.