Which constant must be added and subtracted to solve the quadratic equation 4 x 2-20 x -9-2-0 by the method of completing the square-A- 23B- 25C- 56D- 87

The correct option is B 25 4x^2+20x +9/2=0 Given equation is (2x)^2+(2x)(2)(5)+9/2=0 On putting 2x=y, we have y^2 +10y +9/2=0 y^2+(2)5y+ ( 5 )^2 (5)^2 + 9/2 ...

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Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Completion of Squares Method

Which constan...

Question

Which constant must be added and subtracted to solve the quadratic equation $4 x^{2} + 20 x + \frac{9}{2} = 0$ by the method of completing the square?

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Solution

The correct option is A
25

$4 x^{2} + 20 x + \frac{9}{2} = 0$

Given equation is
$(2 x)^{2} + (2 x) (2) (5) + \frac{9}{2} = 0$
On putting 2x=y, we have $y^{2} + 10 y + \frac{9}{2} = 0$
$y^{2} + (2) 5 y + (5)^{2} - (5)^{2} + \frac{9}{2} = 0$

$(y + 5)^{2} = (5)^{2} - \frac{9}{2}$
$(y + 5)^{2} = 25 - \frac{9}{2}$

Thus,25 must be added and subtracted to solve the given equation.

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Question 7
Which constant must be added and subtracted to solve the quadratic equation $9 x^{2} + \frac{3}{4} x - \sqrt{2} = 0$ by the method of completing the square?
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Question 7
Which constant must be added and subtracted to solve the quadratic equation $9 x^{2} + \frac{3}{4} x - \sqrt{2} = 0$ by the method of completing the square?
(A) $\frac{1}{8}$
(B) $\frac{1}{64}$
(C) $\frac{1}{4}$
(D) $\frac{9}{64}$