Q:

Which are the solutions of x2 = –11x + 4? StartFraction negative 11 minus StartRoot 137 EndRoot Over 2 EndFraction comma StartFraction negative 11 + StartRoot 137 EndRoot Over 2 EndFraction StartFraction negative 11 minus StartRoot 125 EndRoot Over 2 EndFraction comma StartFraction negative 11 + StartRoot 125 EndRoot Over 2 EndFraction StartFraction 11 minus StartRoot 137 EndRoot Over 2 EndFraction comma StartFraction 11 + StartRoot 137 EndRoot Over 2 EndFraction StartFraction 11 minus StartRoot 125 EndRoot Over 2 EndFraction comma StartFraction 11 + StartRoot 125 EndRoot Over 2 EndFraction

Accepted Solution

A:
Answer: [tex]x_1=-\frac{11}{2}-\frac{\sqrt{137} }{2}\\\\x_2=-\frac{11}{2}+\frac{\sqrt{137} }{2}[/tex]Step-by-step explanation: Given the following quadratic equation: [tex]x^2 = -11x + 4[/tex] The steps to solve it are: 1. Move the terms to one side of the equation: [tex]x^2+11x- 4=0[/tex] 2. Apply the Quadratic formula [tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]. In this case we can identify that: [tex]a=1\\b=11\\c=-4[/tex] Then, substituting these values into the Quadratic formula we get the following solutions: [tex]x=\frac{-11\±\sqrt{11^2-4(1)(-4)} }{2(1)}[/tex] [tex]x_1=-\frac{11}{2}-\frac{\sqrt{137} }{2}\\\\x_2=-\frac{11}{2}+\frac{\sqrt{137} }{2}[/tex]