SOLVING QUADRATIC EQUATION : Solving by Completing the Square
Introduction
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.
What do you think - Students? Can you learn? Share your thoughts and experiences in the comment.
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.
- Divide all terms with value of a.
- Isolate the terms in x on one side of the equation.
- Add the square of one-half the coefficient of x or (b2)2 to both sides of the equation.
- Write the square root of both sides of the resulting equation and solve for x.
a)x2−4x=−3 {makesureaispositive1 x2−4x+(−42)2=−3+(−42)2 {add(b2)2=(−42)2=(−2)2︸onleftofequation=4︸onrightofequation x2−4x+(−2)2=−3+4 (x−2)2=1 √(x−2)2=±√1 x−2=±1 x−2=1, x−2=−1 x=3, x=1¯¯
b)−x2+4x+8=0 {makesureaispositive1 −x2−1+4x−1+8−1=0−1 {dividealltermswith-1 x2−4x−8=0 x2−4x=8x2−4x+(−42)2=8+(−42)2 {add(b2)2=(−42)2=(−2)2︸onleftofequation=4︸onrightofequation x2−4x+(−2)2=8+4 (x−2)2=12 √(x−2)2=±√12 x−2=±3.46 x−2=3.46, x−2=−3.46 x=5.46, x=−1.46¯¯
c) 2x2−x−1=0 2x22−x2−12=02 x2−12x−12=0 x2−12x=12x2−12x+(−122)2=12+(−122)2x2−4x+(−14)2=816+(116) (x−14)2=916x−14=±√916 x−2=±3.46 x−2=3.46, x−2=−3.46 x=5.46, x=−1.46¯¯
d) 2x2 − x − 3=02x2 − x − 32 = 02x2 − x2 − 32 = 0x2 − 12x − 32 = 0 x2 − 12x +(−122)2= 32 +(−122)2x2 − 12x +(−14)2= 32 +(−14)2(x − 14)2 = 32+116(x − 14)2 = 2516 (x − 14)2 = 2516√(x − 14)2 = ±√2516x − 14 = ±54x = 14 ± 54x = 64 or x = −44x = 32 or x = −1
Try it yourself - Solving Quadratic Equation : Solving quadratic equation by using Completing the Square
a)4x2−8x−5=0b)2x2−x−6=0c) 12x2−18x=0}ans-x=52,−12ans-x=2,−32ans-x=0,32
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