Solve the equation using any method. x^2-x-30=0 x=square and square

To solve the quadratic equation \(x^2 - x - 30 = 0\), we can use the quadratic formula, which is given by:<br /><br />\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]<br /><br />For the equation \(x^2 - x - 30 = 0\), the coefficients are:<br />- \(a = 1\)<br />- \(b = -1\)<br />- \(c = -30\)<br /><br />Now, substitute these values into the quadratic formula:<br /><br />\[ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-30)}}{2(1)} \]<br />\[ x = \frac{1 \pm \sqrt{1 + 120}}{2} \]<br />\[ x = \frac{1 \pm \sqrt{121}}{2} \]<br />\[ x = \frac{1 \pm 11}{2} \]<br /><br />This gives us two solutions:<br /><br />\[ x = \frac{1 + 11}{2} = \frac{12}{2} = 6 \]<br />\[ x = \frac{1 - 11}{2} = \frac{-10}{2} = -5 \]<br /><br />So, the solutions to the equation \(x^2 - x - 30 = 0\) are:<br /><br />\[ x = 6 \quad \text{and} \quad x = -5 \]