It is not possible to factorize every given quadratic equation.But the method of completing the square is universal.
for a given quadratic equation $ ax^2 + bx + c = 0 $ Steps for completing the square are as follows.
Steps for completing the square method
- divide the coefficient of x term by 2 = b/2a
- add and subtract the square of (b/2) thats $\frac{b^2}{4a^2}$
- complete the square with the terms $ ax^2 + bx +\frac{b^2}{4a^2} = a( x- \frac{b}{2a})^2 $
- take the constant term to right hand side
- solve for x by taking root both sides.
Examples on Completing Square
- $x^2 + 4x - 5 = 0$
the coefficient of x term is 4
so adding and subtracting (4/2)2 = 4
$x^2 + 4x + 4 - 4 - 5 = 0$
$(x^2+ 4x + 4) -9 = 0$
$(x+2)^2 - 9 = 0 $ $(x+2)^2 = x^2 + 4x + 4$
$(x+2)^2 = 3^2 $
take square root both sides
x + 2 = ± 3
x = -2 ± 3
so , x = -2 - 3, -2 + 3
x = -5 , 1
2. $x^2 + 6x - 25 = 0$
the coefficient of x term is 6
so adding and subtracting (6/2)2 = 9
$x^2 + 6x + 9 -9 - 25 = 0$
$(x^2+ 6x + 9) -34 = 0$
$(x+3)^2 - 34 = 0 $ $(x+3)^2 = x^2 + 6x + 9$
$(x+3)^2 = 34 $
take square root both sides
x + 3= ± ? 34
x = -3 ± ? 34
so , x = -3 + ? 34 , -3 - ? 34
Related Tags
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