But we can add a constant d to both sides of the equation to get a new equivalent equation that is a perfect square trinomial. We can't use the square root initially since we do not have c-value. If we instead have an equation on the form of Then you can solve the equation by using the square root of And we found these by completing the square.If you've got a quadratic equation on the form of So therefore, the solutions to the equation □ squared minus 14□ plus 38 equals zero are □ is equal to seven plus root 11 or □ is equal to seven minus root 11. To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b b. So then, we’re left with □ is equal to seven plus or minus root 11. And then if we take the square root of each side, we get □ minus seven is equal to plus or minus the square root of 11.Īnd now into our final stage, which is actually going to be let’s add seven to each side of the equation. So then if we simplify, we get □ minus seven all squared minus 11 is equal to zero.Īnd then our next stage is to actually add 11 to each side of the equation, which gives us □ minus seven all squared is equal to 11. If you square a negative, we get a positive. And we get that again because we had negative seven all squared. So if you add a negative, it’s the same as just subtracting it. To skip ahead: 1) for a quadratic that STARTS WITH X2, skip to time 1:4. Well, negative 14 over two is negative seven. MIT grad shows the easiest way to complete the square to solve a quadratic equation. As we have seen, quadratic equations in this form can easily be solved by extracting roots. So we get □ minus seven all squared and it’s □ minus seven because we had □ plus and then negative 14 over two. This process is called completing the square. Then we still have plus 38 is equal to zero. So the general rule if we have our expression in the form squared plus is that this. So what I’m gonna do is I’m going to recap that first. This question has asked us to solve the equation by completing the square. Solve quadratic equations by factorising, using formulae and completing the square. So far, we have solved quadratic equations by factoring and using the Square Root Property. So if we actually apply this and complete the square of our first two terms, we’re gonna get □ plus and then we’ve got negative 14 over two because a coefficient of our □ is negative 14 and that’s all squared and then minus again negative 14 over two all squared. Solve the equation squared minus 14 plus 38 is equal to zero by completing the square. Solving by completing the square - Higher. If you missed this problem, review Example 7.46. And these two terms are □ squared minus 14□. So if we look back to our equation, we can actually see that it’s the first two terms that are actually gonna apply to completing the square rule too. So the general rule if we have our expression in the form □ squared plus □□ is that this is equal to □ plus □ over two all squared - and that’s because we’ve actually halved the coefficient of □ - and then minus □ over two - again halving the coefficient of □ - and that is all squared. ©Q D2x0o1S2P iKSuGtRa6 4S1oGf1twwuamrUei 0LjLoCM.W T PAMlcl4 drhisg2hatEsB XrqeQsger KvqeidM.2 v 5M1awdPeZ uwjirtbhi QIxnDftiFn4iOteeE qAwlXg1ezbor9aP u2B.w. We know that a quadratic equation in the form of (ax2+bx+c0) can be solved by the factorization method. Create your own worksheets like this one with Infinite Algebra 2. This question has asked us to solve the equation by completing the square. The most common application of completing the square method is factorizing a quadratic equation, and henceforth finding the roots and zeros of a quadratic polynomial or a quadratic equation. Solve the equation □ squared minus 14 □ plus 38 is equal to zero by completing the square.
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