(x%2B5)%3D80.jpeg "(x-3)(x+5)=80")
Solving the Quadratic Equation (x-3)(x+5) = 80
This equation represents a quadratic equation. Let's break down how to solve it:
1. Expanding the Equation
First, we need to expand the left side of the equation by multiplying the terms:
(x - 3)(x + 5) = 80
- x² + 2x - 15 = 80
2. Rearranging the Equation
Now, we need to move all terms to one side to get a standard quadratic equation form:
- x² + 2x - 15 - 80 = 0
- x² + 2x - 95 = 0
3. Solving the Quadratic Equation
We can solve this equation using various methods, including:
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Factoring: Try to find two numbers that multiply to -95 and add up to 2. In this case, it's not easy to factor directly.
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Quadratic Formula: The most reliable way to solve any quadratic equation. The formula is:
- x = (-b ± √(b² - 4ac)) / 2a
Where a = 1, b = 2, and c = -95 from our equation.
4. Applying the Quadratic Formula
Let's plug in the values into the quadratic formula:
- x = (-2 ± √(2² - 4 * 1 * -95)) / (2 * 1)
- x = (-2 ± √(384)) / 2
- x = (-2 ± 19.6) / 2
5. Finding the Solutions
This gives us two possible solutions:
- x₁ = (-2 + 19.6) / 2 = 8.8
- x₂ = (-2 - 19.6) / 2 = -10.8
Conclusion
Therefore, the solutions to the quadratic equation (x - 3)(x + 5) = 80 are x = 8.8 and x = -10.8.