Final answer:
The quadratic equation 2x² + 12x = -5 has two solutions: approximately x ≈ -0.700 and x ≈ -5.800.
Step-by-step explanation:
The quadratic equation 2x² + 12x = -5 can be solved by rearranging it to 2x² + 12x + 5 = 0. Now we can use the quadratic formula to find the solutions of x:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 2, b = 12, and c = 5. Substituting these values, we get:
x = (-12 ± √(12² - 4(2)(5))) / (2(2))
Simplifying further, we have:
x = (-12 ± √(144 - 40)) / 4
x = (-12 ± √(104)) / 4
Since √(104) is approximately 10.198, the solutions for x are:
x ≈ (-12 + 10.198) / 4 ≈ -0.700
x ≈ (-12 - 10.198) / 4 ≈ -5.800