Jasonbradley
Home

(3x-1)^2-(x+3)(2x-1)=7(x+1)(x-2)-3x

3 min read Jun 16, 2024
(3x-1)^2-(x+3)(2x-1)=7(x+1)(x-2)-3x

Solving the Equation: (3x-1)^2-(x+3)(2x-1)=7(x+1)(x-2)-3x

This article will walk you through the steps of solving the equation (3x-1)^2-(x+3)(2x-1)=7(x+1)(x-2)-3x. Let's break it down step by step.

Expanding the Equation

First, we need to expand the equation by multiplying out the parentheses:

  1. (3x-1)^2: This is a square of a binomial. We can use the formula: (a-b)^2 = a^2 - 2ab + b^2

    • (3x-1)^2 = (3x)^2 - 2(3x)(1) + (1)^2 = 9x^2 - 6x + 1

  2. (x+3)(2x-1): This is the product of two binomials. We can use the FOIL method (First, Outer, Inner, Last)

    • (x+3)(2x-1) = 2x^2 - x + 6x - 3 = 2x^2 + 5x - 3

  3. 7(x+1)(x-2): Again, we use the FOIL method

    • 7(x+1)(x-2) = 7(x^2 - 2x + x - 2) = 7(x^2 - x - 2) = 7x^2 - 7x - 14

Now our equation looks like this: 9x^2 - 6x + 1 - (2x^2 + 5x - 3) = 7x^2 - 7x - 14 - 3x

Simplifying the Equation

Next, we simplify the equation by combining like terms:

  1. Remove the parentheses: Remember to distribute the negative sign in front of the second parenthesis

    • 9x^2 - 6x + 1 - 2x^2 - 5x + 3 = 7x^2 - 7x - 14 - 3x

  2. Combine like terms:

    • (9x^2 - 2x^2) + (-6x - 5x) + (1 + 3) = 7x^2 + (-7x - 3x) - 14
    • 7x^2 - 11x + 4 = 7x^2 - 10x - 14

Solving for x

Now we have a simplified equation. Let's solve for x:

  1. Move all terms to one side: Subtract 7x^2 from both sides

    • -11x + 4 = -10x - 14

  2. Combine like terms: Add 10x to both sides

    • -x + 4 = -14

  3. Isolate x: Subtract 4 from both sides

    • -x = -18

  4. Solve for x: Multiply both sides by -1

    • x = 18

Solution

Therefore, the solution to the equation (3x-1)^2-(x+3)(2x-1)=7(x+1)(x-2)-3x is x = 18.

Related Post

Featured Posts