Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Quadratic Formula

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

Given quadratic equation:

$x^2-3x-5=0$

Define the variables:

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

Substitute the defined variables into the quadratic formula and solve for x:

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

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

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

Therefore, the exact solutions to the given quadratic equation are:

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

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Answer 2

Answer:

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

Step-by-step explanation:

Quadratic Formula :

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

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

Here,

• a = 1
• b = -3
• c = -5

Solving :

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

Hence, the solutions are :

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