(2x-3)%3D2(x%2B1)-in-standard-form.jpeg "(x+5)(2x-3)=2(x+1) In Standard Form")
Solving a Quadratic Equation in Standard Form
This article will guide you through the process of solving the equation (x+5)(2x-3) = 2(x+1) and writing it in standard form.
Step 1: Expand the equation
Begin by expanding both sides of the equation to remove the parentheses:
- Left side: (x+5)(2x-3) = 2x² - 3x + 10x - 15 = 2x² + 7x - 15
- Right side: 2(x+1) = 2x + 2
This simplifies the equation to: 2x² + 7x - 15 = 2x + 2
Step 2: Move all terms to one side
To put the equation in standard form, we need all terms on one side, setting the equation equal to zero:
2x² + 7x - 15 - 2x - 2 = 0
Step 3: Combine like terms
Combine the x terms and the constant terms:
2x² + 5x - 17 = 0
Step 4: Standard Form
The equation is now in standard quadratic form: ax² + bx + c = 0, where a = 2, b = 5, and c = -17.
Therefore, the standard form of the equation (x+5)(2x-3) = 2(x+1) is 2x² + 5x - 17 = 0.
Further Steps
From here, you can solve for x using various methods, such as:
- Factoring: If the equation can be factored, you can find the values of x that make the equation true.
- Quadratic Formula: This formula can be used to find the solutions for any quadratic equation.
- Completing the Square: This method involves manipulating the equation to form a perfect square trinomial.