To solve this quadratic equation \(x^2 - 25x + 144 = 0\), we can factor the equation or use the quadratic formula.
1. Factor the equation:
The quadratic equation can be factored as:
\(x^2 - 25x + 144 = (x-9)(x-16) = 0\)
Setting each factor to zero gives:
\(x-9 = 0\) or \(x-16 = 0\)
So, \(x = 9\) or \(x = 16\)
Therefore, the solutions to the equation are \(x = 9\) and \(x = 16\).
2. Use the Quadratic Formula:
The quadratic formula is given by:
For the equation \(ax^2 + bx + c = 0\), the solutions are given by:
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
In this case, a = 1, b = -25, and c = 144. Substituting these values into the formula:
\(x = \frac{-(-25) \pm \sqrt{(-25)^2 - 4(1)(144)}}{2(1)}\)
\(x = \frac{25 \pm \sqrt{625 - 576}}{2}\)
\(x = \frac{25 \pm \sqrt{49}}{2}\)
\(x = \frac{25 \pm 7}{2}\)
This gives us two possible solutions:
\(x = \frac{25 + 7}{2} = 16\) or \(x = \frac{25 - 7}{2} = 9\)
Therefore, the solutions to the equation \(x^2 - 25x + 144 = 0\) are \(x = 9\) and \(x = 16\).
x^2-25x+144=0
1 answer