Answer:
Answer: w is 1.6 or. -5.6
Step-by-step explanation:
• I guess the question asks to find the value of w
[tex]{ \rm{3w + {w}^{2} + 1 = 10 - w }}[/tex]
• arrange the equation in a quadratic equation format. i.e; ax² + bx + c = 0
[tex]{ \rm{ {w}^{2} + (3w + w) + 1 - 10 = 0 }} \\ \\ { \rm{ {w}^{2} + 4w - 9 = 0 }}[/tex]
• let's solve the equation using the quadratic formular
[tex] \hookrightarrow \: { \tt{w = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }} \\ [/tex]
• Substitute following the mathematical operation rules:
[tex]{ \rm{w = \frac{ - 4 \pm \sqrt{ {4}^{2} - (4 \times 1 \times - 9) } }{(2 \times 1)} }} \\ \\ { \rm{w = \frac{ - 4 \pm \sqrt{52} }{2} }}[/tex]
• split the result:
[tex]{ \rm{either \: \{w = \frac{ - 4 + \sqrt{52} }{2} \} \: \: or \: \: \{w = \frac{ - 4 - \sqrt{52} }{2} \} }} \\ \\ { \rm{either \: \{w = 1.6 \} \: \: or \: \: \{w = - 5.6 \}}}[/tex]
