Question

2.
Which constant should be added and
subtracted to solve the quadratic equation
(2x)2 - 7x + 5 = 0 by the method of completing the square?
(a) 7/2
(b) 7/4
(c) 49/4
(d) none of these ​

Answer 1

Answer:

Completing the Square

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .

To solve ax2+bx+c=0 by completing the square:

1. Transform the equation so that the constant term, c , is alone on the right side.

2. If a , the leading coefficient (the coefficient of the x2 term), is not equal to 1 , divide both sides by a .

3. Add the square of half the coefficient of the x -term, (b2a)2 to both sides of the equation.

4. Factor the left side as the square of a binomial.

5. Take the square root of both sides. (Remember: (x+q)2=r is equivalent to x+q=±r√ .)

6. Solve for x .

Example 1:

Solve x2−6x−3=0 by completing the square.

x2−6x=3x2−6x+(−3)2=3+9(x−3)2=12x−3=±12−−√           =±23√x=3±23√

Example 2:

Solve: 7x2−8x+3=0

7x2−8x=−3x2−87x=−37x2−87x+(−47)2=−37+1649(x−47)2=−549x−47=±5√7ix=47±5√7i(x−3)2=12x−3=±12−−√           =±23√x=3±23√

Answer 2

2×(7/2) ^2-7×7/2=0

2×49/4-49/2=0

49/2-49/2=0

0=0

Hence the answer is 7/2