1 / 5

Solving Quadratic Equations Through Factoring and Multiplying Brackets

Explore the process of solving quadratic equations by multiplying out brackets and factoring expressions. This guide walks you through several quadratic equations, demonstrating how to simplify complex expressions and solve for x step-by-step. Learn how to carefully deal with negative signs and mathematical fractions while avoiding common pitfalls. Whether you are looking to enhance your algebra skills or need help with specific problems, this resource provides clear guidance and practical examples to help you master solving quadratics.

haruki
Télécharger la présentation

Solving Quadratic Equations Through Factoring and Multiplying Brackets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2 2 + = 6 x-2 x+1 2(x+1) + 2(x-2) = 6 (x-2)(x+1) (x-2)(x+1) 2(x+1) + 2(x-2) = 6 4x + 2 + 4x – 4 = 6 (x²-x-2) 8x -2 = 6x² -6x -12 0 = 6x² - 14x - 10 3x² - 7x - 5 = 0 Multiply out those brackets! OOH! – I could make those numbers easier to work with Now solve that quadratic!

  2. x 2 = ½ + x-2 x+1 2(x+1) + x(x-2) = ½ (x-2)(x+1) 2(x+1) + x(x-2) = ½ 4x + 2 + x² – 2x = ½ (x²-x-2) 2(x² +2x + 2) = 1(x² - x – 2) 2x² + 4x + 4 = x² - x - 2 x² + 5x +6 = 0 (x-2)(x+1) Multiply out those brackets! Deal with that fraction! Now solve that quadratic!

  3. 4 x = 6 x-2 x+1 x(x+1) - 4(x-2) = 6 (x-2)(x+1) (x-2)(x+1) x(x+1) - 4(x-2) = 6 x² + x - 4x + 8 = 6 (x²-x-2) x² - 3x + 8= 6x² -6x -12 0 = 5x² - 3x - 20 Multiply out those brackets – watch out for that negative sign! Now solve that quadratic!

  4. 4 x+3 + = 6 x²-9 x+1 2(x+1) + 2(x²-9) = 6 (x²-9)(x+1) EEK! – THIS WILL MULTIPLY OUT TO MAKE A CUBIC! – WE NEED TO AVOID THIS. LET’S START AGAIN!

  5. 4 x+3 - = 6 x²-9 x+1 LET’S FACTORISE! x+3 4 - = 6 x+1 (x+3)(x-3) 1 4 - = 6 (x-3) x+1 Multiply out those brackets – watch out for those negative signs! (x+1) - 4(x-3) = 6 (x-3)(x+1) Quadratic to solve is 0 = 6x² - 9x – 31 (x-3)(x+1) = 6 (x+1) - 4(x-3) x + 1 - 4x +12 = 6(x²-3x+x-3)

More Related