Explore IDNLearn.com's extensive Q&A database and find the answers you need. Ask anything and receive prompt, well-informed answers from our community of experienced experts.
Sagot :
Answer:
The solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
Step-by-step explanation:
Given the expression
3x² – 2x = 5
Solving with the quadratic formula
[tex]3x^2-2x=5[/tex]
subtract 5 from both sides
[tex]3x^2-2x-5=5-5[/tex]
Simplify
[tex]3x^2-2x-5=0[/tex]
For a quadratic equation of the form ax²+bx+c=0
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For a = 3, b = -2, c = -5
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \:8}{2\cdot \:3}[/tex]
Separate the solutions
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3},\:x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
solving
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3}[/tex]
[tex]=\frac{2+8}{2\cdot \:3}[/tex]
[tex]=\frac{10}{6}[/tex]
[tex]=\frac{5}{3}[/tex]
also solving
[tex]x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
[tex]=\frac{2-8}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{6}[/tex]
[tex]=-\frac{6}{6}[/tex]
[tex]=-1[/tex]
Therefore, the solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.