Perfect Square Quadratic Equation Examples

Perfect Square Quadratic Equation Examples First recall the algebraic identities We shall use these identities to carry out the process called Completing the Square For example consider the quadratic function What can be added to yield a perfect square Using the previous identities we see that if we put 2 e 8 that is e 4 it is enough to add to generate a perfect square

Example 1 Factoring x 2 8 x 16 Notice that both the first and last terms are perfect squares x 2 x 2 and 16 4 2 Additionally notice that the middle term is two times the product of the numbers that are squared 2 x 4 8 x Example Solve 5x 2 6x 1 0 Coefficients are a 5 b 6 c 1 Quadratic Formula x b 177 b2 4ac 2a Put in a b and c x 6 177 62 4 215 5 215 1 2 215 5 Solve x 6 177 36 20 10 x 6 177 16 10 x 6 177 4 10 x 0 2 or 1 Answer x 0 2 or x 1

A perfect quadratic square has only one solution and touches the x axis The quadratic equation y x 178 can be moved in the horizontal direction by change the value of h in the equation for a perfect quadratic square y x h 178 Perfect quadratic squares are investigated using interactive examples and exercises

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Perfect Square Quadratic Equation Examples

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9 3 Solve Quadratic Equations By Completing The Square

https://math.libretexts.org/Bookshelves/Algebra
Feb 14 2022 0183 32 Find left frac 1 2 cdot b right 2 the number needed to complete the square Add it to both sides of the equation Factor the perfect square trinomial writing it as a binomial squared on the left and simplify by adding the terms on the right Use the Square Root Property Simplify the radical and then solve the two resulting equations

Completing The Square video Khan Academy

https://www.khanacademy.org/math/algebra/x2f8bb
Some quadratic expressions can be factored as perfect squares For example x 178 6x 9 x 3 178 However even if an expression isn t a perfect square we can turn it into one by adding a constant number

10 5 Solving Quadratic Equations Using The Method Of Completing The Square

https://math.libretexts.org/Bookshelves/Algebra
Jun 4 2023 0183 32 We need another method for solving quadratic equations The method we shall study is based on perfect square trinomials and extraction of roots The method is called solving quadratic equations by completing the square Consider the equation x2 6x 5 0 10 5 1 10 5 1 x 2 6 x 5 0

Completing The Square Method Formula Examples Cuemath

https://www.cuemath.com/algebra/completing-the-square
Completing the square formula is the formula required to convert a quadratic polynomial or equation into a perfect square with some additional constant It is expressed as ax 2 bx c a x m 2 n where m and n are real numbers What is the Use of Completing the Square Formula

10 2 Solve Quadratic Equations By Completing The Square

https://math.libretexts.org/Bookshelves/Algebra
Feb 13 2022 0183 32 Definition SOLVE A QUADRATIC EQUATION OF THE FORM x 2 bx c 0 BY COMPLETING THE SQUARE Isolate the variable terms on one side and the constant terms on the other Find frac 1 2 183 b 2 the number to complete the square Add it to both sides of the equation Factor the perfect square trinomial as a

Example Let us find the roots of the same equation that was mentioned in the earlier section x 2 3x 4 0 using the quadratic formula a 1 b 3 and c 4 x b 177 b 2 4ac 2a 3 177 3 2 4 1 4 2 1 3 177 25 2 3 177 5 2 3 5 2 or 3 5 2 8 2 or 2 2 4 or 1 are the roots This video is trying to show you that there is a pattern that you can use to factor a perfect square trinomial If you multiply a b 2 you always get a 2 2ab b 2 You can leverage that pattern to reverse the process Start with a 2 2ab b 2 Let s use a specfic example 4x 2 20x 25 Is 4x 2 a perfect square Yes It is 2x 2

Algebra Examples Quadratic Equations Finding the Perfect Square Trinomial Step by Step Examples Algebra Quadratic Equations Find the Perfect Square Trinomial 4x2 5x 4 x 2 5 x Factor out the 4 4 4 x2 5x 4 4 x 2 5 x 4 To find the c c value c b 2 2 c b 2 2 divide the coefficient of x x by 2 2 and square the result