Question

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

Answer 1

Answer:

D. {-3, and -2.5}

Step-by-step 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:

$\Longrightarrow: \sf{AX^2+BX+C=0}\\\\\\\Longrightarrow: \sf{x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

• A=2
• B=11
• C=15

$\sf{x_{1,\:2}=\dfrac{-11\pm \sqrt{11^2-4\cdot \:2\cdot \:15}}{2\cdot \:2}}$

Solve.

Use the order of operations.

PEMDAS

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

$\sf{\sqrt{11^2-4\cdot \:2\cdot \:15}}$

Multiply the numbers from left to right.

4*2*15=120

$:\Longrightarrow\sf{\sqrt{11^2-120}$

Do exponents.

11²=11*11=121

$\Longrightarrow: \sf{\sqrt{121-120}$

Subtract the numbers from left to right.

121-120=1

$\sf{\sqrt{1}}=1$

$\sf{x_{1,\:2}=\dfrac{-11\pm \:1}{2\cdot \:2}}$

$\Longrightarrow: \sf{x_1=\dfrac{-11+1}{2\cdot \:2},\:x_2=\dfrac{-11-1}{2\cdot \:2}}$

Solve.

$\sf{\dfrac{-11+1}{2\cdot \:2}}=\dfrac{-10}{2*2}=\dfrac{-10}{4}=-\dfrac{10}{4}$

$\sf{\dfrac{-10\div2}{4\div2}=\dfrac{-5}{2}=-\dfrac{5}{2} }$

Divide is another options.

-5/2=-2.5

$\sf{\dfrac{-11-1}{2\cdot \:2}}$

Solve.

$\Longrightarrow: \sf{\dfrac{-11-1}{2\cdot \:2}}=\dfrac{-12}{2*2}=\dfrac{-12\div4}{4\div4}=\dfrac{-3}{1}=-3$

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.