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Mrac [35]
2 years ago
5

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

Mathematics
1 answer:
Mandarinka [93]2 years ago
4 0

Answer:

<u>Answer</u><u>:</u><u> </u><u>w</u><u> </u><u>is</u><u> </u><u>1</u><u>.</u><u>6</u><u> </u><u> </u><u>or</u><u>. </u><u>-</u><u>5</u><u>.</u><u>6</u><u> </u>

Step-by-step 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 \times 1 \times  - 9) } }{(2 \times 1)} }} \\  \\ { \rm{w =  \frac{ - 4 \pm \sqrt{52} }{2} }}

• split the result:

{ \rm{either \:  \{w =  \frac{ - 4 +  \sqrt{52} }{2} \} \:  \: or \:  \:  \{w =  \frac{ - 4 -  \sqrt{52} }{2}  \} }} \\  \\ { \rm{either \:  \{w = 1.6 \} \:  \: or \:  \:  \{w =  - 5.6 \}}}

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