(x-7)-(x-4)(x%2B4)%3D11.jpeg "(x+3)(x-7)-(x-4)(x+4)=11")
Solving the Equation: (x+3)(x-7)-(x-4)(x+4)=11
This article will guide you through the steps of solving the equation (x+3)(x-7)-(x-4)(x+4)=11.
Expanding the Equation
First, we need to expand the equation by multiplying the terms in the brackets. We'll use the FOIL method (First, Outer, Inner, Last) for this:
-
(x+3)(x-7):
- First: x * x = x²
- Outer: x * -7 = -7x
- Inner: 3 * x = 3x
- Last: 3 * -7 = -21
- Combining terms: x² - 7x + 3x - 21 = x² - 4x - 21
-
(x-4)(x+4):
- First: x * x = x²
- Outer: x * 4 = 4x
- Inner: -4 * x = -4x
- Last: -4 * 4 = -16
- Combining terms: x² + 4x - 4x - 16 = x² - 16
Now, we can substitute these expanded terms back into the original equation:
(x² - 4x - 21) - (x² - 16) = 11
Simplifying the Equation
Next, we'll simplify the equation by removing the brackets and combining like terms:
x² - 4x - 21 - x² + 16 = 11
-4x - 5 = 11
Isolating the Variable
Our goal is to isolate the variable 'x'. We start by moving the constant term to the right side of the equation:
-4x = 11 + 5
-4x = 16
Solving for x
Finally, we divide both sides of the equation by -4 to solve for 'x':
x = 16 / -4
x = -4
Conclusion
Therefore, the solution to the equation (x+3)(x-7)-(x-4)(x+4)=11 is x = -4.