Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Answer:
[tex]x=2\\x=-\frac{1}{2}[/tex]
Step-by-step explanation:
1) Move terms to the left side.
[tex]3x=2x^{2} -2\\3x-(2x^{2}-2)=0[/tex]
2) Distribute.
[tex]3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0[/tex]
3) Rearrange terms.
[tex]3x-2x^{2} +2=0\\-2x^{2} +3x+2=0[/tex]
4) Common factor.
[tex]-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0[/tex]
5) Divide both sides of the equation by the same term.
[tex]-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0[/tex]
6) Use the quadratic formula.
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
[tex]2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2[/tex]
[tex]x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}[/tex]
7) Simplify.
Evaluate the exponent
[tex]x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]
Multiply the numbers
[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]
Add the numbers
[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{25} }{2*2}[/tex]
Evaluate the square root
[tex]x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}[/tex]
Multiply the numbers
[tex]x=\frac{3+5}{2*2}[/tex]
[tex]x=\frac{3+5}{4}[/tex]
8) Seperate the equations.
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
[tex]x=\frac{3+5}{4}[/tex]
[tex]x=\frac{3-5}{4}[/tex]
9) Solve.
Rearrange and isolate the variable to find each solution.
[tex]x=2\\x=-\frac{1}{2}[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
