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 \(x = 3\).