Question

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}

Answer 1

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.