(x-3)%3D-4x.jpeg "(2x+1)(x-3)=-4x")
Solving the Equation: (2x + 1)(x - 3) = -4x
This article will guide you through the steps of solving the equation (2x + 1)(x - 3) = -4x.
1. Expanding the Equation
First, we need to expand the left side of the equation by multiplying the two binomials:
(2x + 1)(x - 3) = 2x² - 6x + x - 3
Simplify the expression:
2x² - 5x - 3 = -4x
2. Bringing all terms to one side
Now, move all the terms to the left side of the equation to make it a quadratic equation:
2x² - 5x - 3 + 4x = 0
Simplify:
2x² - x - 3 = 0
3. Solving the Quadratic Equation
We can solve the quadratic equation by using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Where a = 2, b = -1, and c = -3.
Substitute the values into the formula:
x = [1 ± √((-1)² - 4 * 2 * -3)] / (2 * 2)
x = [1 ± √(25)] / 4
x = [1 ± 5] / 4
Therefore, we have two possible solutions:
x1 = (1 + 5) / 4 = 3/2
x2 = (1 - 5) / 4 = -1
4. Verification
Finally, we need to verify if these solutions are valid by plugging them back into the original equation:
For x = 3/2:
(2 * 3/2 + 1)(3/2 - 3) = -4 * 3/2
(4)( -3/2) = -6
-6 = -6 (True)
For x = -1:
(2 * -1 + 1)(-1 - 3) = -4 * -1
(-1)(-4) = 4
4 = 4 (True)
Therefore, both solutions x = 3/2 and x = -1 are valid solutions for the equation (2x + 1)(x - 3) = -4x.