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What is the solution set for 2x2 + 15 = -11x?

a {-5, -1.5}
b {2.5, 3}
c {1.5, 5}
d {-3, -2.5}

User Mdominick
by
8.1k points

1 Answer

6 votes

Answer:

D. {-3, and -2.5}

Explanation:

Using the quadratic equation, you can find the solution to 2x2+15=-11x.


\sf{2x^2+15=-11x}

First, you have to add by 11x from both sides.


\Longrightarrow: \sf{2x^2+15+11x=-11x+11x}

Solve.

2x²+11x+15=0

Use the quadratic formula.

Quadratic formula:


\Longrightarrow: \sf{AX^2+BX+C=0}\\\\\\\Longrightarrow: \sf{x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)}

  • A=2
  • B=11
  • C=15


\sf{x_(1,\:2)=(-11\pm √(11^2-4\cdot \:2\cdot \:15))/(2\cdot \:2)}

Solve.

Use the order of operations.

PEMDAS

  • Parentheses
  • Exponents
  • Multiply
  • Divide
  • Add
  • Subtract


\sf{√(11^2-4\cdot \:2\cdot \:15)}

Multiply the numbers from left to right.

4*2*15=120


:\Longrightarrow\sf{√(11^2-120)

Do exponents.

11²=11*11=121


\Longrightarrow: \sf{√(121-120)

Subtract the numbers from left to right.

121-120=1


\sf{√(1)}=1


\sf{x_(1,\:2)=(-11\pm \:1)/(2\cdot \:2)}


\Longrightarrow: \sf{x_1=(-11+1)/(2\cdot \:2),\:x_2=(-11-1)/(2\cdot \:2)}

Solve.


\sf{(-11+1)/(2\cdot \:2)}=(-10)/(2*2)=(-10)/(4)=-(10)/(4)


\sf{(-10/2)/(4/2)=(-5)/(2)=-(5)/(2) }

Divide is another options.

-5/2=-2.5


\sf{(-11-1)/(2\cdot \:2)}

Solve.


\Longrightarrow: \sf{(-11-1)/(2\cdot \:2)}=(-12)/(2*2)=(-12/4)/(4/4)=(-3)/(1)=-3

Solutions:


\Longrightarrow: \boxed{\sf{-3, \ -2.5}}

  • Therefore, the correct answer is "D. {-3, -2.5}".

I hope this helps. Let me know if you have any questions.

User Jeff Gilfelt
by
8.2k points

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