Thank you for visiting Solve the equation using any method tex x 2 3x 8 0 tex A 1 70 4 70 B 1 70 4 70 C 1. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We want to solve the quadratic equation
[tex]$$
x^2 - 3x - 8 = 0.
$$[/tex]
A standard method for solving quadratic equations is to use the quadratic formula. For an equation of the form
[tex]$$
ax^2 + bx + c = 0,
$$[/tex]
the solutions are given by
[tex]$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
$$[/tex]
In our equation, we have [tex]$a = 1$[/tex], [tex]$b = -3$[/tex], and [tex]$c = -8$[/tex]. Plugging these values into the quadratic formula gives:
[tex]$$
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-8)}}{2 \cdot 1}.
$$[/tex]
First, compute the discriminant (the expression under the square root):
[tex]$$
\Delta = (-3)^2 - 4(1)(-8) = 9 + 32 = 41.
$$[/tex]
Thus, the formula becomes:
[tex]$$
x = \frac{3 \pm \sqrt{41}}{2}.
$$[/tex]
Now, to find approximate values, we evaluate [tex]$\sqrt{41}$[/tex]. We have:
[tex]$$
\sqrt{41} \approx 6.40.
$$[/tex]
Substitute this approximate value back into the solution:
1. For the solution with the minus sign:
[tex]$$
x \approx \frac{3 - 6.40}{2} = \frac{-3.40}{2} \approx -1.70.
$$[/tex]
2. For the solution with the plus sign:
[tex]$$
x \approx \frac{3 + 6.40}{2} = \frac{9.40}{2} \approx 4.70.
$$[/tex]
Thus, the solutions to the equation are approximately
[tex]$$
x \approx -1.70 \quad \text{and} \quad x \approx 4.70.
$$[/tex]
So, the answer is
[tex]$$
\{-1.70,\, 4.70\}.
$$[/tex]
[tex]$$
x^2 - 3x - 8 = 0.
$$[/tex]
A standard method for solving quadratic equations is to use the quadratic formula. For an equation of the form
[tex]$$
ax^2 + bx + c = 0,
$$[/tex]
the solutions are given by
[tex]$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
$$[/tex]
In our equation, we have [tex]$a = 1$[/tex], [tex]$b = -3$[/tex], and [tex]$c = -8$[/tex]. Plugging these values into the quadratic formula gives:
[tex]$$
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-8)}}{2 \cdot 1}.
$$[/tex]
First, compute the discriminant (the expression under the square root):
[tex]$$
\Delta = (-3)^2 - 4(1)(-8) = 9 + 32 = 41.
$$[/tex]
Thus, the formula becomes:
[tex]$$
x = \frac{3 \pm \sqrt{41}}{2}.
$$[/tex]
Now, to find approximate values, we evaluate [tex]$\sqrt{41}$[/tex]. We have:
[tex]$$
\sqrt{41} \approx 6.40.
$$[/tex]
Substitute this approximate value back into the solution:
1. For the solution with the minus sign:
[tex]$$
x \approx \frac{3 - 6.40}{2} = \frac{-3.40}{2} \approx -1.70.
$$[/tex]
2. For the solution with the plus sign:
[tex]$$
x \approx \frac{3 + 6.40}{2} = \frac{9.40}{2} \approx 4.70.
$$[/tex]
Thus, the solutions to the equation are approximately
[tex]$$
x \approx -1.70 \quad \text{and} \quad x \approx 4.70.
$$[/tex]
So, the answer is
[tex]$$
\{-1.70,\, 4.70\}.
$$[/tex]
Thank you for reading the article Solve the equation using any method tex x 2 3x 8 0 tex A 1 70 4 70 B 1 70 4 70 C 1. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
