(x-3)-(2x-5)(x%2B3)%3Dx(x-5).jpeg "(x+2)(x-3)-(2x-5)(x+3)=x(x-5)")
Solving the Equation: (x+2)(x-3)-(2x-5)(x+3)=x(x-5)
This article will guide you through the steps of solving the given equation:
(x+2)(x-3)-(2x-5)(x+3)=x(x-5)
Expanding the Equation
To begin, we need to expand the products on both sides of the equation:
- Left Side:
- (x+2)(x-3) = x² - x - 6
- (2x-5)(x+3) = 2x² + x - 15
- Right Side:
- x(x-5) = x² - 5x
Now the equation becomes:
x² - x - 6 - (2x² + x - 15) = x² - 5x
Simplifying the Equation
Next, we simplify the left side by distributing the negative sign:
x² - x - 6 - 2x² - x + 15 = x² - 5x
Combining like terms on the left side gives:
-x² - 2x + 9 = x² - 5x
Rearranging and Solving
To solve for x, we need to bring all the terms to one side. Let's move all terms to the left side:
-x² - 2x + 9 - x² + 5x = 0
Combining like terms:
-2x² + 3x + 9 = 0
Now we have a quadratic equation. We can solve this using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a = -2
- b = 3
- c = 9
Substituting these values into the quadratic formula:
x = (-3 ± √(3² - 4 * -2 * 9)) / (2 * -2)
x = (-3 ± √(9 + 72)) / -4
x = (-3 ± √81) / -4
x = (-3 ± 9) / -4
This gives us two possible solutions:
- x = (-3 + 9) / -4 = -1.5
- x = (-3 - 9) / -4 = 3
Conclusion
Therefore, the solutions to the equation (x+2)(x-3)-(2x-5)(x+3)=x(x-5) are x = -1.5 and x = 3.