Question

solve the quadratic equation: $3x^2 + 12x - 9 = 0$. use the keypad to enter your answer in the box. additional symbols can be found using the drop - down arrows at the top of the keypad. $x = \square$

Explanation:

Step1: Simplify the quadratic equation

Divide all terms by 3:
$$x^2 + 4x - 3 = 0$$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=1$, $b=4$, $c=-3$

Step3: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute values:
$$x=\frac{-4\pm\sqrt{4^2-4(1)(-3)}}{2(1)}$$

Step4: Calculate discriminant

$$\sqrt{16 + 12}=\sqrt{28}=2\sqrt{7}$$

Step5: Simplify the expression

$$x=\frac{-4\pm2\sqrt{7}}{2}=-2\pm\sqrt{7}$$

Answer:

$x=-2+\sqrt{7}$ or $x=-2-\sqrt{7}$