CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Solving a Quadratic Equation by Completion of Squares Method

Solve for x.2...

Question

Solve for x.
$2^{2 x + 3} = 65 (2^{X} - 2) + 122$

Open in App

Solution

$2^{2 x + 3} = {65.2}^{x} - 130 + 122$
$2^{2 x} \times 2^{3} = {65.2}^{x} - 8 L e t 2^{x} = t \Rightarrow t^{2} \times 8 = 64. t - 8$
$\Rightarrow 8 t^{2} - 65 t + 8 = 0 \Rightarrow 8 t^{2} - 64 t - t + 8 = 0 \Rightarrow 8 + (t - 8) - 1 (t - 8) = 0 \Rightarrow (8 t - 1) (t - 8) = 0 \Rightarrow t = \frac{1}{8}, 8 \Rightarrow 2^{x} = \frac{1}{8}, 2^{x} = 8 2^{x} = \frac{1}{2^{3}}, 2^{x} = 2^{3} 2^{x} = 2^{- 3} 2^{x} = 2^{3} \Rightarrow x = 3 2^{x} = 2^{- 3}, x = 3$

Suggest Corrections

thumbs-up

5

Similar questions

Q. Solve the following equations:

2^{2 x + 3} - 57 = 65 (2^{x} - 1)

.

2^{2 x + 3} = 65 (2^{x} - 1) + 57

Q. Solve for x :

\frac{(x + 2) (2 x - 3) - 2 x^{2} + 6}{x - 5} = 2.

5 x - 2 (2 x - 3) = 2 (3 x - 1) + \frac{5}{2}

Q. Solve the inequality for real

x

2 (2 x + 3) - 10 < 6 (x - 2)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Solving QE by Completing the Square

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Solving a Quadratic Equation by Completion of Squares Method

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon