Answer:
Step-by-step explanation:
Using the quadratic equation, you can find the solution to 2x2+15=-11x.
[tex]\sf{2x^2+15=-11x}[/tex]
First, you have to add by 11x from both sides.
[tex]\Longrightarrow: \sf{2x^2+15+11x=-11x+11x}[/tex]
Solve.
2x²+11x+15=0
Use the quadratic formula.
Quadratic formula:
[tex]\Longrightarrow: \sf{AX^2+BX+C=0}\\\\\\\Longrightarrow: \sf{x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\sf{x_{1,\:2}=\dfrac{-11\pm \sqrt{11^2-4\cdot \:2\cdot \:15}}{2\cdot \:2}}[/tex]
Solve.
Use the order of operations.
PEMDAS
[tex]\sf{\sqrt{11^2-4\cdot \:2\cdot \:15}}[/tex]
Multiply the numbers from left to right.
4*2*15=120
[tex]:\Longrightarrow\sf{\sqrt{11^2-120}[/tex]
Do exponents.
11²=11*11=121
[tex]\Longrightarrow: \sf{\sqrt{121-120}[/tex]
Subtract the numbers from left to right.
121-120=1
[tex]\sf{\sqrt{1}}=1[/tex]
[tex]\sf{x_{1,\:2}=\dfrac{-11\pm \:1}{2\cdot \:2}}[/tex]
[tex]\Longrightarrow: \sf{x_1=\dfrac{-11+1}{2\cdot \:2},\:x_2=\dfrac{-11-1}{2\cdot \:2}}[/tex]
Solve.
[tex]\sf{\dfrac{-11+1}{2\cdot \:2}}=\dfrac{-10}{2*2}=\dfrac{-10}{4}=-\dfrac{10}{4}[/tex]
[tex]\sf{\dfrac{-10\div2}{4\div2}=\dfrac{-5}{2}=-\dfrac{5}{2} }[/tex]
Divide is another options.
-5/2=-2.5
[tex]\sf{\dfrac{-11-1}{2\cdot \:2}}[/tex]
Solve.
[tex]\Longrightarrow: \sf{\dfrac{-11-1}{2\cdot \:2}}=\dfrac{-12}{2*2}=\dfrac{-12\div4}{4\div4}=\dfrac{-3}{1}=-3[/tex]
Solutions:
[tex]\Longrightarrow: \boxed{\sf{-3, \ -2.5}}[/tex]
I hope this helps. Let me know if you have any questions.
