Final answer:
The equation to solve is 4x² + 12x + 10 = 0, which can be solved using the quadratic formula. However, the discriminant in this quadratic equation is negative, indicating that there are no real solutions. The provided multiple-choice options may be incorrect if they imply that a real solution exists.
Step-by-step explanation:
The question asks to solve the equation 4x(x+3) = -10. First, let's distribute the 4 to both terms inside the parentheses: 4x² + 12x = -10. After rearranging the equation, we have 4x² + 12x + 10 = 0. This quadratic equation is in the form ax² + bx + c = 0, where a = 4, b = 12, and c = 10.
To solve this, we can use the quadratic formula, which is given by x = (-b ± √(b² - 4ac))/(2a). Substituting the values of a, b, and c, we get x = (-12 ± √(144 - 4×4×10))/(2×4). Calculating the discriminant (√(144 - 160)) will lead us to a negative number inside the square root, which suggests there are no real solutions for this equation. Since the choices provided suggest the anticipation of real solutions, it's possible that the original equation or the options given contain an error. This equation can be solved using the quadratic formula. For an equation of the form ax² + bx + c = 0, the solutions can be found using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, the equation is 4x(x+3) = -10. Expanding the equation gives 4x² + 12x = -10. Subtracting -10 from both sides gives 4x² + 12x + 10 = 0. Comparing this to the general form ax² + bx + c = 0, we have a = 4, b = 12, and c = 10.
Substituting these values into the quadratic formula, we get:
x = (-12 ± √(12² - 4(4)(10))) / (2(4))
Simplifying further, we have:
x = (-12 ± √(144 - 160)) / 8
x = (-12 ± √(-16))/8
Since the value inside the square root is negative, the solutions are imaginary.