QUADRATIC EQUATION BY COMPLETING THE SQUARE METHOD
At some point it is difficult to solve some quadratic equation by factorization some expression is even impossible to factorize, in such case you switch to completing the square method.
To find the roots of a quadratic equation in the form:
\{a}{x}^{2}+{b}{x}+{c}={0}ax2+bx+c=0,
follow these steps:
(i) If a does not equal \{1}1, divide each side by a (so that the coefficient of the x2 is \{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
To find the roots of a quadratic equation in the form:
\{a}{x}^{2}+{b}{x}+{c}={0}ax2+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
Consider 2X2 – 11x + 12 = 0
Step1
Separate the constant and variable containing elements into different sides of the equality sign
2X2 – 11x = -12
Step2
Divide both side by the coefficient of x2
X2 – x = -6
Also learn how to solve quadratic equation by factorizing
Step3
Add the square of half of the coefficient of x to both side of the equation
X2 – x + (-
)2 = -6 +
(x – )2 –
(x – )2 –
Taking the square root of both sides
X – = ±
X = ±
X = and x =
X = and x =
X =4 and x =
The following must be noted whenever completing the square method is use
The coefficient of x2 must be reduce to 1
The constant (value independent on x must be moved to the right hand side of the equation.
Every quadratic equation must have two roots either unique or the same
So now try your hands on this one 3X2 – 13x + 10 = 0
Answer is and 1