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(3x+5)+(x+2) ^(2)+ (3x+5)-(x+2) ^(2)=20x^(2)-78

2 min read Jun 16, 2024
(3x+5)+(x+2) ^(2)+ (3x+5)-(x+2) ^(2)=20x^(2)-78

Solving the Equation: (3x+5)+(x+2)^(2)+(3x+5)-(x+2)^(2)=20x^(2)-78

This article will guide you through the steps to solve the given equation: (3x+5)+(x+2)^(2)+(3x+5)-(x+2)^(2)=20x^(2)-78

Simplifying the Equation

  1. Identify similar terms: Notice that (x+2)^(2) appears twice, once with a positive sign and once with a negative sign. These terms will cancel each other out.

  2. Combine like terms: After canceling out the (x+2)^(2) terms, we are left with: (3x + 5) + (3x + 5) = 20x^(2) - 78

  3. Simplify further: Combine the terms on the left side: 6x + 10 = 20x^(2) - 78

Rearranging the Equation

  1. Move all terms to one side: Subtract 6x and 10 from both sides to get a standard quadratic equation: 20x^(2) - 6x - 88 = 0

Solving the Quadratic Equation

  1. Factor the equation: The quadratic equation can be factored as: (10x + 22)(2x - 4) = 0

  2. Set each factor to zero: To find the solutions, we need to set each factor equal to zero: 10x + 22 = 0 or 2x - 4 = 0

  3. Solve for x: Solve each equation for x: x = -22/10 = -11/5 or x = 4/2 = 2

Conclusion

Therefore, the solutions to the equation (3x+5)+(x+2)^(2)+(3x+5)-(x+2)^(2)=20x^(2)-78 are x = -11/5 and x = 2.

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