Which are the solutions of x^2=-5x+8 7 (-5-sqrt (57))/(2),(-5+sqrt (57))/(2) (-5-sqrt (7))/(2),(-5+sqrt (7))/(2) (5-sqrt (57))/(2),(5+sqrt (57))/(2) (5-sqrt (7))/(2),(5+sqrt (7))/(2)

To solve the quadratic equation \(x^2 = -5x + 8\), we first rewrite it in standard form:<br /><br />\[ x^2 + 5x - 8 = 0 \]<br /><br />Next, we use the quadratic formula to find the solutions. The quadratic formula is given by:<br /><br />\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]<br /><br />For the equation \(x^2 + 5x - 8 = 0\), the coefficients are:<br />- \(a = 1\)<br />- \(b = 5\)<br />- \(c = -8\)<br /><br />Substituting these values into the quadratic formula, we get:<br /><br />\[ x = \frac{-5 \pm \sqrt{5^2 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1} \]<br />\[ x = \frac{-5 \pm \sqrt{25 + 32}}{2} \]<br />\[ x = \frac{-5 \pm \sqrt{57}}{2} \]<br /><br />Thus, the solutions are:<br /><br />\[ x = \frac{-5 - \sqrt{57}}{2} \quad \text{and} \quad x = \frac{-5 + \sqrt{57}}{2} \]<br /><br />Therefore, the correct answer is:<br /><br />\[ \frac{-5 - \sqrt{57}}{2}, \frac{-5 + \sqrt{57}}{2} \]