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Let us study this in detail using illustrations in the following sections. These formulas are derived geometrically. To complete the square in the expression ax 2 + bx + c, first find the values of m and n using the above formulas and then substitute these values in: ax 2 + bx + c = a(x + m) 2 + n. Instead of using the complex step-wise method for completing the square, we can use the following simple formula to complete the square. The formula for completing the square is: ax 2 + bx + c ⇒ a(x + m) 2 + n, where
![solving quadratic equations by completing the square solving quadratic equations by completing the square](https://www.chilimath.com/wp-content/uploads/2019/02/qcompsqr-ex3b.png)
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Note: Completing the square formula is used to derive the quadratic formula.Ĭompleting the square formula is a technique or method that can also be used to find the roots of the given quadratic equations, ax 2 + bx + c = 0, where a, b and c are any real numbers but a ≠ 0. A quadratic expression in variable x: ax 2 + bx + c, where a, b and c are any real numbers but a ≠ 0, can be converted into a perfect square with some additional constant by using completing the square formula or technique. Add and subtract (b/2a) 2 after the 'x' term and simplify.Ĭompleting the square formula is a technique or method to convert a quadratic polynomial or equation into a perfect square with some additional constant.Note: To complete the square in an expression ax 2 + bx + c Step 5: Simplify the last two numbers.Step 4: Factorize the perfect square trinomial formed by the first 3 terms using the identity x 2 + 2xy + y 2 = (x + y) 2.Step 3: Add and subtract the above number after the x term in the expression whose coefficient of x 2 is 1.Step 2: Find the square of the above number.
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