Solve the quadratic equation $5x^2 = - 16x - 12$ by factorisation method.
- $x=2, \cfrac{6}{5}$
- $x=2, \cfrac{5}{6}$
- $x=-2, -\cfrac{5}{6}$
- $x=-2, -\cfrac{6}{5}$
Reveal answer
Fill a bubble to check yourself
D
Correct answer
Explanation
5x^2 + 16x + 12 = 0. Factoring: 5x^2 + 10x + 6x + 12 = 0. 5x(x+2) + 6(x+2) = 0. (5x+6)(x+2) = 0. Roots are x = -2 and x = -6/5.
AI explanation
Rewrite the equation as 5x squared + 16x + 12 equals 0. Using the factorisation method, we split the middle term by finding two numbers that multiply to 5 times 12 (which is 60) and add to 16, giving 6 and 10. The equation becomes 5x squared + 10x + 6x + 12 equals 0, which factors into 5x(x + 2) + 6(x + 2) equals 0. This gives (5x + 6)(x + 2) equals 0, so x equals negative 6 divided by 5 or x equals negative 2. The roots are x equals negative 2 and x equals negative 6 divided by 5.