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Here is your complete step-by-step tutorial to solving quadratic equations using the completing the square formula (3 step method). The guide includes a free completing the square worksheets, examples and practice problems, and a video tutorial.
Completing the square refers to finding a constant “C” that you can add to the first two terms to make a perfect square trinomial, which can be factored into the expression (+). The number you get at this step is the constant that completes the square.
Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
Express the trinomial as a square of binomial, and combine the constants to get the final answer. Convert the quadratic equation of the form y=ax^2+bx+c to the vertex form using the completing the square method. Use easy to follow examples to help you understand the process better!
What is Completing the Square Formula? Completing the square formula is the formula required to convert a quadratic polynomial or equation into a perfect square with some additional constant. It is expressed as, ax 2 + bx + c ⇒ a(x + m) 2 + n, where, m and n are real numbers.
Solve by completing the square: Non-integer solutions. Solve equations by completing the square. Worked example: completing the square (leading coefficient ≠ 1) Completing the square. Solving quadratics by completing the square: no solution. Proof of the quadratic formula. Solving quadratics by completing the square.
Completing the square is a way of rearranging quadratic equations from the general form ax 2 + bx + c = 0 to the vertex form a(x – h) 2 + k = 0. It is written as a(x + m) 2 + n, such that the left side is a perfect square trinomial.