Solve using the quadratic formula.You will define 1) x^2+3x-10=0 discrimina perfect s

To solve the quadratic equation \(x^2 + 3x - 10 = 0\) using the quadratic formula, we first identify the coefficients: \(a = 1\), \(b = 3\), and \(c = -10\).<br /><br />The quadratic formula is given by:<br /><br />\[<br />x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}<br />\]<br /><br />First, calculate the discriminant (\(b^2 - 4ac\)):<br /><br />\[<br />b^2 - 4ac = 3^2 - 4 \times 1 \times (-10) = 9 + 40 = 49<br />\]<br /><br />Since the discriminant is 49, which is a perfect square, the solutions will be real and rational.<br /><br />Now, apply the quadratic formula:<br /><br />\[<br />x = \frac{-3 \pm \sqrt{49}}{2 \times 1} = \frac{-3 \pm 7}{2}<br />\]<br /><br />This gives us two solutions:<br /><br />1. \(x = \frac{-3 + 7}{2} = \frac{4}{2} = 2\)<br /><br />2. \(x = \frac{-3 - 7}{2} = \frac{-10}{2} = -5\)<br /><br />Therefore, the solutions to the equation \(x^2 + 3x - 10 = 0\) are \(x = 2\) and \(x = -5\).