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![]() ![]() ![]() If you get stuck on the fractions, the right-hand term in the parentheses will be half of the x-term. We especially designed this trinomial to be a perfect square so that this step would work: Now rewrite the perfect square trinomial as the square of the two binomial factors You only need to solve for the x squared term. ![]() When you do not have an x term because b 0, the equation is easier to solve. X² + 5x +25/4 = 28/4 → Hey, that is equal to 7 Continue to solve this quadratic equation with the completing the square method described above. That is 5/2 which is 25/4 when it is squared Now we complete the square by dividing the x-term by 2 and adding the square of that to both sides of the equation. X² + 5x = 3/4 → I prefer this way of doing it Or, you can divide EVERY term by 4 to get ĭivide through the x² term and x term by 4 to factor it out So, we have to divide the x² AND the x terms by 4 to bring the coefficient of x² down to 1. In the example following rule 2 that we were supposed to try, the coefficient of x² is 4. As shown in rule 2, you have to divide by the value of a (which is 4 in your case). You are correct that you cannot get rid of it by adding or subtracting it out. ![]() We have 5 5 5 in the original equation and 9 9 9 in the perfect square.This would be the same as rule 2 (and everything after that) in the article above. 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. Thus, our problem can be rewritten as ( x + 2 ) 2 = 0 (x+2)^2 = 0 ( x + 2 ) 2 = 0. 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. Solve by completing the square: x 2 + 4 x + 4 = 0 x^2 + 4x + 4 = 0 x 2 + 4 x + 4 = 0. Let's discuss a few examples of solving quadratic equations by completing the square.Įxample 1.
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