Answer:
the two x-values for the equation 2x^2 + 11x + 15 = 0 are x = -2.5 and x = -3.
Explanation:
To find the two x-values for the equation 2x^2 + 11x + 15 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = 11, and c = 15. Substituting these values into the quadratic formula, we get:
x = (-(11) ± √((11)^2 - 4(2)(15))) / (2(2))
Simplifying the equation further, we have:
x = (-11 ± √(121 - 120)) / 4
x = (-11 ± √1) / 4
Now, we can simplify the square root term:
√1 = 1
Therefore, the equation becomes:
x = (-11 ± 1) / 4
Now, we have two cases to consider:
Case 1: x = (-11 + 1) / 4
Simplifying the equation, we get:
x = -10 / 4
x = -2.5
Case 2: x = (-11 - 1) / 4
Simplifying the equation, we get:
x = -12 / 4
x = -3
Hence, the two x-values for the equation 2x^2 + 11x + 15 = 0 are x = -2.5 and x = -3.