Completing the Square Method

Sometimes the roots of a quadratic equation cannot be obtained by simple factorization. So, a more general method is used. This method, which is based on the fact that any quadratic equation may be written in the form of (x+p)² = q, where p and q are real numbers, is known as completing the square method.

Question:-

Solve the equation by completing the square method.

2x²-7x+9=(x-3)(x+1)+3x

Answer:-

2x²-7x+9 = x²+x-3x-3+3x
-x²-x+3 -x²-x+3
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x²-8x+12 = 0

now we solve this quadratic equation by completing the square method

x²-8x=-12

x²-8x+(8/2)²=(8/2)²-12

x²-8x+16 = 16-12

(x-4)² = 4

taking the square root on both sides, square root symbol looks like √ .

√(x-4)²= √4

x-4 = ±2

We also can use square root calculator to get these values.

x-4 = +2 or x-4 = -2

x=6 or x=2 is the answer

This equation have just one variable.similarly we can also work on linear equations in two variables