(x-2)-(4x-3)(x%2B5)%3Dx(x-9).jpeg "(x+1)(x-2)-(4x-3)(x+5)=x(x-9)")
Solving the Equation: (x+1)(x-2)-(4x-3)(x+5)=x(x-9)
This article will guide you through the process of solving the equation (x+1)(x-2)-(4x-3)(x+5)=x(x-9).
Step 1: Expand the products
We begin by expanding the products on both sides of the equation:
- (x+1)(x-2) = x² - x - 2
- (4x-3)(x+5) = 4x² + 17x - 15
- x(x-9) = x² - 9x
Now, the equation becomes: (x² - x - 2) - (4x² + 17x - 15) = x² - 9x
Step 2: Simplify the equation
Next, we simplify the equation by removing the parentheses and combining like terms:
- x² - x - 2 - 4x² - 17x + 15 = x² - 9x
- -3x² - 18x + 13 = x² - 9x
Step 3: Move all terms to one side
To solve for x, we need to move all terms to one side of the equation:
- -3x² - 18x + 13 - x² + 9x = 0
- -4x² - 9x + 13 = 0
Step 4: Solve the quadratic equation
We now have a quadratic equation in the form of ax² + bx + c = 0. To solve this, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In our equation, a = -4, b = -9, and c = 13. Substituting these values into the quadratic formula, we get:
x = (9 ± √((-9)² - 4 * -4 * 13)) / (2 * -4)
x = (9 ± √(81 + 208)) / -8
x = (9 ± √289) / -8
x = (9 ± 17) / -8
This gives us two possible solutions:
- x = (9 + 17) / -8 = -3.25
- x = (9 - 17) / -8 = 1
Conclusion
Therefore, the solutions to the equation (x+1)(x-2)-(4x-3)(x+5)=x(x-9) are x = -3.25 and x = 1.