solve for x: 2xcubed+18x=-15xsquared
18x^3 + 15x^2 + 18x = 0
3x(6x^2 + 5x + 6) = 0
so x = 0 or x = ...... (use the quadratic formula, I see imaginary roots coming up here )
just noticed it was
2x^3 + 15x^2 + 18x = 0
x(2x^2 + 15x + 18) = 0
x(2x+3)(x+6) = 0
x = 0 or x = -3/2 or x = -6
To solve the equation 2x^3 + 18x = -15x^2 for x, we need to rearrange the equation and set it equal to zero. Here's how you can solve it step-by-step:
1. Start by moving all terms to one side of the equation to form a polynomial equal to zero:
2x^3 + 15x^2 + 18x = 0
2. Factor out the common factor, if any, from the equation. In this case, the common factor is x:
x(2x^2 + 15x + 18) = 0
3. Now, we can solve for x by setting each factor equal to zero:
x = 0 (Equation 1)
2x^2 + 15x + 18 = 0 (Equation 2)
4. Solve Equation 1:
x = 0
5. Solve Equation 2 by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). In our case, a = 2, b = 15, and c = 18.
x = (-15 ± √(15^2 - 4*2*18)) / (2*2)
x = (-15 ± √(225 - 144)) / 4
x = (-15 ± √81) / 4
x = (-15 ± 9) / 4
6. Solve the two possible values for x:
x1 = (-15 + 9) / 4 = -6 / 4 = -3/2
x2 = (-15 - 9) / 4 = -24 / 4 = -6
Therefore, the solutions to the equation 2x^3 + 18x = -15x^2 are x = 0, x = -6, and x = -3/2.