Chapter 11: Q. 94 E (page 1069)

Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises , solve by completing the square.
$y^{2} - 14 = 6 y$

Short Answer

Expert verified

The required value of $y$ is $3 + \sqrt{23}, 3 - \sqrt{23}$

Step by step solution

Given information

$y^{2} - 14 = 6 y$

Calculation

$y^{2} - 14 = 6 y \Rightarrow y^{2} - 6 y = 14 \Rightarrow y^{2} - 6 y + (\frac{1}{2} \times {(- 6))}^{2} = 14 + 9 \Rightarrow y^{2} - 6 y + 9 = 14 + 9 \Rightarrow {(y - 3)}^{2} = 23 \Rightarrow y - 3 = \pm \sqrt{23} \Rightarrow y = 3 \pm \sqrt{23} = 3 + \sqrt{23}, 3 - \sqrt{23}$

The required value of $y$ is $3 + \sqrt{23}, 3 - \sqrt{23}$

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Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises , solve by completing the square.
$y^{2} - 14 = 6 y$

Short Answer

Step by step solution

Given information

Calculation

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Solve quadratic equations of the form x2+bx+c=0by completing the square.In the following exercises , solve by completing the square.y2-14=6y

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Probability and Statistics

Mechanics Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises , solve by completing the square.
$y^{2} - 14 = 6 y$