X2-7x+12=0

To solve the quadratic equation $x^2 - 7x + 12 = 0$, we can factorize it or use the quadratic formula. Here, I will show you both methods. 1. Factoring method: We need to find two numbers that multiply to 12 and add up to -7. These numbers are -4 and -3. Therefore, we can rewrite the equation as: $(x - 4)(x - 3) = 0$ Setting each factor to zero gives us the solutions: $x - 4 = 0$ or $x - 3 = 0$ Solving for x: $x = 4$ or $x = 3$ So, the solutions to the equation $x^2 - 7x + 12 = 0$ are $x = 4$ and $x = 3$. 2. Quadratic formula method: The quadratic formula is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ For the given equation $x^2 - 7x + 12 = 0$, the coefficients are: $a = 1$, $b = -7$, and $c = 12$ Plugging these values into the quadratic formula: $x = \frac{7 \pm \sqrt{(-7)^2 - 4*1*12}}{2*1}$ $x = \frac{7 \pm \sqrt{49 - 48}}{2}$ $x = \frac{7 \pm 1}{2}$ This gives us two possible solutions: $x = \frac{7 + 1}{2} = 4$ and $x = \frac{7 - 1}{2} = 3$ So, the solutions to the equation $x^2 - 7x + 12 = 0$ are $x = 4$ and $x = 3$.