Completing The Square Flashcards, test questions and answers

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What is Completing The Square?

Completing the square is a technique used in algebra to solve for an unknown variable. It essentially involves rearranging a quadratic equation into its standard form, which can then be solved using the quadratic formula. This process is called completing the square because it involves adding terms and simplifying so that one side of the equation forms a perfect square trinomial. The general form of a quadratic equation is ax^2 + bx + c = 0, where ‘a’, ‘b’, and ‘c’ are constants. To complete the square, we first need to add half of b squared to both sides of this equation: (ax^2 + bx + c) + (1/2)(b^2) = (1/2)(b^2). Then we subtract c from both sides and factor out x on each side: [ax^2 + (b/2)^2] – [(c – 1/2(b^3))/a] = 0. Finally, we take the left-hand side of this new expression and rewrite it as a perfect square trinomial by multiplying all terms inside brackets by 2 over 4 times ‘a’: [ax+[(b/(4*a))]^ 2]. Once you have completed the square, you can use the Quadratic Formula to find solutions for x. The Quadratic Formula states that given any quadratic equation in two variables ax²+ bx+ c=0 , solutions for x can be found through plugging numbers into this formula: x=(-b ± √(b²-4ac)) / 2a . With your newly completed perfect square trinomial on one side of your original equation, simply substitute those values into your formula to find your solution. In conclusion, completing the Square offers an efficient way of solving certain types of equations without having to resort to more complicated techniques like factoring or graphing. By taking advantage of this useful tool in algebraic problem solving, students can gain deeper insight into mathematical principles while developing their critical thinking skills at the same time.