Final Answer:
The solution to 2x^2 + 12x = 10 is a. -3 ± √14.
Step-by-step explanation:
Move the constant term to the right side:
2x^2 + 12x - 10 = 0
Factor out the greatest common factor:
2(x^2 + 6x - 5) = 0
Factor the quadratic expression:
2(x + 5)(x - 1) = 0
Solve for x using the zero factor property:
x + 5 = 0 or x - 1 = 0
x = -5 or x = 1
Combine solutions:
x = -5 ± √14
Therefore, the solution to the equation is -3 ± √14.
Option d (-3 ± √29) is incorrect because the square root of 29 is not a factor of 10. Options b and c are incorrect because the coefficient of x in the quadratic expression is 12, not 6, resulting in a different square root term.