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SOLVING QUADRATIC EQUATION : Solving by Completing the Square

Introduction
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Apart from factoring method and quadratic formula, quadratic equation can be solved by using Completing the Square method.

How to solve - Solving Quadratic Equation : Solving by Completing the Square?

To solve a quadratic equation by completing the square.
  1. Divide all terms with value of a.
  2. Isolate the terms in x on one side of the equation.
  3. Add the square of one-half the coefficient of x or (b2)2 to both sides of the equation.
  4. Write the square root of both sides of the resulting equation and solve for x.
Example : Solve the following by using completing the square method.

a)x24x=3{makesureaispositive1x24x+(42)2=3+(42)2{add(b2)2=(42)2=(2)2onleftofequation=4onrightofequationx24x+(2)2=3+4(x2)2=1(x2)2=±1x2=±1x2=1,x2=1x=3,x=1¯¯

b)x2+4x+8=0{makesureaispositive1x21+4x1+81=01{dividealltermswith-1x24x8=0x24x=8x24x+(42)2=8+(42)2{add(b2)2=(42)2=(2)2onleftofequation=4onrightofequationx24x+(2)2=8+4(x2)2=12(x2)2=±12x2=±3.46x2=3.46,x2=3.46x=5.46,x=1.46¯¯

c)2x2x1=02x22x212=02x212x12=0x212x=12x212x+(122)2=12+(122)2x24x+(14)2=816+(116)(x14)2=916x14=±916x2=±3.46x2=3.46,x2=3.46x=5.46,x=1.46¯¯


d)2x2x3=02x2x32=02x2x232=0x212x32=0x212x+(122)2=32+(122)2x212x+(14)2=32+(14)2(x14)2=32+116(x14)2=2516(x14)2=2516(x14)2=±2516x14=±54x=14±54x=64orx=44x=32orx=1
Try it yourself - Solving Quadratic Equation : Solving quadratic equation by using Completing the Square

a)4x28x5=0b)2x2x6=0c)12x218x=0}ans-x=52,12ans-x=2,32ans-x=0,32

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