Question

So I have this question I cannot figure out 3w+w2+1=10−w

Answer 1

Answer: w is 1.6 or. -5.6

Explanation:

• I guess the question asks to find the value of w

`{ \rm{3w + {w}^(2) + 1 = 10 - w }}`

• arrange the equation in a quadratic equation format. i.e; ax² + bx + c = 0

`{ \rm{ {w}^(2) + (3w + w) + 1 - 10 = 0 }} \\ \\ { \rm{ {w}^(2) + 4w - 9 = 0 }}`

• let's solve the equation using the quadratic formular

`\hookrightarrow \: { \tt{w = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac} }{2a} }} \\`

• a is 1
• b is 4
• c is -9

• Substitute following the mathematical operation rules:

`{ \rm{w = \frac{ - 4 \pm \sqrt{ {4}^(2) - (4 * 1 * - 9) } }{(2 * 1)} }} \\ \\ { \rm{w = ( - 4 \pm √(52) )/(2) }}`

• split the result:

`{ \rm{either \: \{w = ( - 4 + √(52) )/(2) \} \: \: or \: \: \{w = ( - 4 - √(52) )/(2) \} }} \\ \\ { \rm{either \: \{w = 1.6 \} \: \: or \: \: \{w = - 5.6 \}}}`