![]() We have 5 5 5 in the original equation and 9 9 9 in the perfect square. To produce these terms by squaring a linear binomial, we can use: ( x + 3 ) 2 = x 2 + 6 x + 9 (x + 3)^2 = x^2 + 6x + 9 ( x + 3 ) 2 = x 2 + 6 x + 9.Īs you can see, the third term doesn't agree with what we have in our equations, so we need to complete the square. ![]() Let's take a look at the part containing the unknown x x x we have x 2 + 6 x x^2 + 6x x 2 + 6 x. Solve using the completing the square method: x 2 + 6 x + 5 = 0 x^2 + 6x + 5 = 0 x 2 + 6 x + 5 = 0. In fact, in this example we didn't have to complete the square, because the perfect square trinomial was already there, staring at us defiantly!Įxample 2. To factor the equation, you need to first follow this equation: x2 + 2ax + a2. Thus, our problem can be rewritten as ( x + 2 ) 2 = 0 (x+2)^2 = 0 ( x + 2 ) 2 = 0. Step 2: If a is not equal to 1, divide the complete equation by a such that the coefficient of x2. Step 1: Write the equation in the form, such that c is on the right side. Solve By Factoring Example: 3x2-2x-10 Complete The Square Example: 3x2-2x-10 (After you click the example, change the Method to 'Solve By Completing the Square'. Then follow the given steps to solve it by completing the square method. There are different methods you can use to solve quadratic equations, depending on your particular problem. We immediately recognize the short multiplication formula working in reverse: ( x + 2 ) 2 = x 2 + 4 x + 4 (x+2)^2 =x^2 + 4x + 4 ( x + 2 ) 2 = x 2 + 4 x + 4. Suppose ax2 + bx + c 0 is the given quadratic equation. Solve by completing the square: x 2 + 4 x + 4 = 0 x^2 + 4x + 4 = 0 x 2 + 4 x + 4 = 0. You can complete the square to rearrange a more complicated quadratic formula or even to solve a quadratic equation. Solve any quadratic equation by completing the square. ![]() Let's discuss a few examples of solving quadratic equations by completing the square.Įxample 1.
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