Solve the equation by completing the square. If the solutions are real, give exact and approximate answers. Otherwise, list the exact solutions. 2y^2=-12y-3 Please help!!!!!!:(
2y^2 + 12y = -3
y^2 + 6y = -3/2
y^2 + 6y + 9 = 15/2
(y + 3)^2 = 15/2
To solve the equation by completing the square, follow these steps:
Step 1: Move all terms to one side of the equation to set it equal to zero.
2y^2 + 12y + 3 = 0
Step 2: Divide the entire equation by the coefficient of y^2 to make the leading coefficient 1.
y^2 + 6y + 3/2 = 0
Step 3: To complete the square, take half of the coefficient of y (6), square it (36), and add it to both sides of the equation.
y^2 + 6y + 9 + 3/2 = 9
y^2 + 6y + 9 + 3/2 = 18/2
(y + 3)^2 + 3/2 = 9
Step 4: Write the quadratic equation in the form (x - h)^2 = k, where (h, k) is the vertex of the parabola.
(y + 3)^2 = 9 - 3/2
(y + 3)^2 = 15/2
Step 5: Take the square root of both sides of the equation to solve for y.
y + 3 = ±√(15/2)
Step 6: Solve for y by subtracting 3 from both sides.
y = -3 ± √(15/2)
Therefore, the solutions to the equation 2y^2 = -12y - 3 obtained by completing the square are:
y = -3 + √(15/2)
y = -3 - √(15/2)
To get the approximate answers, you can calculate the numerical value using a calculator or use a decimal approximation for √(15/2) and perform the addition and subtraction.