(x%2B5)%3D18.jpeg "(x-2)(x+5)=18")
Solving the Equation (x-2)(x+5) = 18
This equation represents a quadratic equation, which is an equation with the highest power of the variable being 2. To solve it, we need to manipulate it to get a standard quadratic equation in the form of ax² + bx + c = 0.
1. Expanding the Equation:
First, we expand the left side of the equation by multiplying the terms:
(x - 2)(x + 5) = 18 x² + 3x - 10 = 18
2. Rearranging to Standard Form:
Next, we move the constant term from the right side to the left side to get the equation in standard form:
x² + 3x - 10 - 18 = 0 x² + 3x - 28 = 0
3. Solving the Quadratic Equation:
Now we have a standard quadratic equation, which can be solved by various methods:
- Factoring: We can try to factor the equation by finding two numbers that add up to 3 (the coefficient of the x term) and multiply to -28 (the constant term). In this case, the numbers are 7 and -4. Therefore, the factored form of the equation is: (x + 7)(x - 4) = 0
This means that either x + 7 = 0 or x - 4 = 0. Solving for x gives us: x = -7 or x = 4
- Quadratic Formula: If factoring is difficult, we can use the quadratic formula to solve for x: x = (-b ± √(b² - 4ac)) / 2a
Where a = 1, b = 3, and c = -28. Substituting these values into the formula gives us:
x = (-3 ± √(3² - 4 * 1 * -28)) / 2 * 1 x = (-3 ± √(121)) / 2 x = (-3 ± 11) / 2
Therefore, x = (-3 + 11) / 2 = 4 or x = (-3 - 11) / 2 = -7
4. Solutions:
The solutions to the equation (x - 2)(x + 5) = 18 are x = 4 and x = -7.