(x-7)%3D-3x.jpeg "(x+7)(x-7)=-3x")
Solving the Equation: (x+7)(x-7) = -3x
This equation involves expanding the left-hand side and then solving the resulting quadratic equation. Here's how we can break down the process:
Expanding the Equation
First, we expand the left side of the equation by applying the distributive property (or FOIL method):
(x + 7)(x - 7) = -3x
- (x * x) + (x * -7) + (7 * x) + (7 * -7) = -3x
- x² - 7x + 7x - 49 = -3x
Now, simplify the equation by combining like terms:
- x² - 49 = -3x
Rearranging and Solving
To solve this quadratic equation, we need to set it equal to zero:
- x² + 3x - 49 = 0
This equation can be solved using the quadratic formula:
- x = (-b ± √(b² - 4ac)) / 2a
Where 'a', 'b', and 'c' are the coefficients of the quadratic equation (a = 1, b = 3, c = -49).
Substitute the values into the quadratic formula:
- x = (-3 ± √(3² - 4 * 1 * -49)) / (2 * 1)
- x = (-3 ± √(205)) / 2
- x = (-3 ± √205) / 2
Therefore, the solutions to the equation are:
- x = (-3 + √205) / 2
- x = (-3 - √205) / 2
Conclusion
We have successfully solved the equation (x+7)(x-7) = -3x by expanding the left side, rearranging it into a standard quadratic form, and then applying the quadratic formula. The solutions to this equation are x = (-3 + √205) / 2 and x = (-3 - √205) / 2.