![]() (x-a)^2 is basically the format of the answer you want receive. Notice that now I could factorise the left hand side into (x - 2)^2 I want to factorise the left side of the equal sign, so I have to find a value for (something) which would allow me to factorise the left-hand side of the equation. Situations could vary, but this is the basic idea behind the procedure. Finally, you add 1 to both sides, taking into account that 4 could be positive OR negative. Next, you want to take the square root from both sides so that x-1 is equal to the positive or negative square root of 16 (positive or negative 4). This will all give you the equation (x-1)^2=16. Because you´re taking this value away from the constant, you will add it to the other side of the equation (this might not make sense at first, but if the constant were on the variable side, you would be subtracting). In this case, you will add 1 because it perfectly factors out into (x-1)^2. Next, you want to add a value to the variable side so that when you factor that side, you will have a perfect square. Because there is a 3 in front of x^2, you will divide both sides by 3 to get x^2-2x=5. ![]() Next, you want to get rid of the coefficient before x^2 (a) because it won´t always be a perfect square. To do this, you will subtract 8 from both sides to get 3x^2-6x=15. To complete the square, first, you want to get the constant (c) on one side of the equation, and the variable(s) on the other side. Solve the equation below using the method of completing the square.You don´t need another video because I´m about to explain it to you! Say you have the equation 3x^2-6x+8=23. Solve the following equation by completing the squareĭetermine the square roots on both sides. Rewrite the quadratic equation by isolating c on the right side.Īdd both sides of the equation by (10/2) 2 = 5 2 = 25.ĭivide each term of the equation by 3 to make the leading coefficient equals to 1.Ĭomparing with the standard form (x + b/2) 2 = -(c-b 2/4)Ĭ – b2/4 = 2/3 – = 2/3 – 25/36 = -1/36Īdd (1/2 × −5/2) = 25/16 to both sides of the equation.įind the square roots on both sides of the equation ![]() ![]() The standard form of completing square is Solve by completing square x 2 + 4x – 5 = 0 Transform the equation x 2 + 6x – 2 = 0 to (x + 3) 2 – 11 = 0 Solve the following quadrating equation by completing square method: Now let’s solve a couple of quadratic equations using the completing square method. Isolate the term c to right side of the equation Given a quadratic equation ax 2 + bx + c = 0 The quadratic formula is derived using a method of completing the square. Completing the Square Formula is given as: ax 2 + bx + c ⇒ (x + p) 2 + constant. In mathematics, completing the square is used to compute quadratic polynomials.
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