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Yanka [14]
2 years ago
5

Find the exact solutions of x2 − 3x − 5 = 0 using the quadratic formula. Show all work! 75 points please help!!!!!

Mathematics
2 answers:
noname [10]2 years ago
8 0

Answer:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Step-by-step explanation:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0

<u>Given quadratic equation</u>:

x^2-3x-5=0

<u>Define the variables</u>:

\implies a=1, \quad b=-3, \quad c=-5

<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:

\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}

\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}

\implies x=\dfrac{3 \pm \sqrt{29}}{2}

Therefore, the exact solutions to the given <u>quadratic equation</u> are:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Learn more about the quadratic formula here:

brainly.com/question/27868610

brainly.com/question/27750885

Papessa [141]2 years ago
6 0

Answer:

\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}

Step-by-step explanation:

<u>Quadratic Formula</u> :

\boxed {\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}

We are given the equation x² - 3x - 5 = 0.

Here,

  • a = 1
  • b = -3
  • c = -5

<u>Solving</u> :

  • 3 ± √3² - 4(1)(-5) / 2(1)
  • 3 ± √29 / 2

<u>Hence, the solutions are</u> :

\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}

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Step-by-step explanation:

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We can solve for x shown below:

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SHOW YOUR WORK!!<br><br> What is the distance between point A (-3, -2) and Point B (4, -7)?
gulaghasi [49]

Answer: \bold{\sqrt{74}}

<u>Step-by-step explanation:</u>

\text{Use the distance formula: }d_AB=\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}\\where\ (X_A, y_A)=(-3, -2)\\and\ (x_B,y_B)=(4, -7)\\\\\\d_AB=\sqrt{(-3-4)^2+[-2-(-7)]^2}\\\\.\quad =\sqrt{(-7)^2+(5)^2}\\\\.\quad =\sqrt{49+25}\\\\.\quad =\boxed{\sqrt{74}}

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