Question

Explain the $\sf{"Completing \: square \: method"}$ with any one example.

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Answer 1

Let us take an equation

2x²-7x+3=0

1.) First eleminate the coffiecient of x²

Divide by 2

x² - 7/2 x +3/2 = 0

x² -7/2 x = -3/2

We gonna make it (a+b)²

Trick → Add the square of half the coffiecient of x on both sides.

So add (-7/4)² on both sides

x² - 7/2 x + (-7/4) = -3/2 +(-7/4)²

x² - 2 (x)(-7/4) - (-7/4) = -3/2 +49/16

(x-7/4)² = 25/16

Square root both sides

x-7/4 = ±5/4

x = +5/4+7/4
x = 3

x = -5/4+7/4
x = 1/2

Answer 2

Answer:

x = 3/4, -1.

Step-by-step explanation:

What is completing square method:

It is a method used to solve a Quadratic equation by changing the form of the equation so that the left hand side is a perfect square trinomial.

Example:

Solve 4x² + x - 3 = 0 by completing the square method.

1. Coefficient of x² should be 1:

Given Equation is 4x² + x = 3.

Divide the Entire Equation by the coefficient of x^(4), we get

x² + (x/4) = (3/4)

2. Add the square of half the coefficient of 'x' on both sides.

x² + (x/4) + (1/8)² = (3/4) + (1/8)²

x² + (x/4) + (1/64) = (3/4) + (1/64)

3. Three terms on the left side will be in the form of a² + 2ab + b²

(x)² + 2 * (x)(1/4) + (1/8)² = (3/4) + (1/64)

(x + 1/8)² = 49/64.

4. Solve for x by simplification:

(x + 1/8) = ±7/8

(i)

When x = +7/8:

⇒ x + 1/8 = 7/8

⇒ x = 7/8 - 1/8

⇒ x = 6/8

⇒ x = 3/4

(ii)

When x = -7/8:

⇒ x + 1/8 = -7/8

⇒ x = -7/8 - 1/8

⇒ x = -8/8

⇒ x = -1.

Therefore, x = 3/4, -1 are the roots of the equation.

Hope it helps!