Chapter 6: Q. 304 (page 627)

Solve the following exercise
$14 y^{2} - 77 y = - 35$

Short Answer

Expert verified

The solution of the given equation is $y = \frac{1}{2} o r y = 5$ $14 y^{2} - 77 y = - 35$

Step by step solution

Step 1. given information

The given equation $14 y^{2} - 77 y = - 35$

Step 2. Simplify the quadratic equation

Simplifying the given equation

$(a - b) (a + b) = 0 a - b = 0 o r a + b = 0 a = - b o r a = b Simplify the quadratic expression : 14 y^{2} - 77 y = - 35 [Given the expression] 14 y^{2} - 77 y + 35 = 0 [Write the quadratic equation of standard form] 7 (2 y^{2} - 11 y + 5) = 0 [Factor out 7 from expression] 7 (2 y^{2} - 10 y - y + 5) = 0 [Since; - 11 - - 10 y - y] 7 (2 y (y - 5) - 1 (y - 5)) = 0 [Factor out the common factor from group] 7 (2 y - 1) (y - 5) = 0 [Factor the common factor from expression] 7 ≃ 0 o r 2 y - 1 - 0 o r y - 5 - 0 [Use the zero product property] o r y = 1 / 2 o r y = 5$

Step 3. Checking the equation

$Check Substitute them value y = 1 / 2 in the original equation . 14 y^{2} - 77 y = - 35 [G i v e n e q u a t i o n] 14 \times (\frac{1}{2})^{2} - 77 (\frac{1}{2}) = - 35 [P u t y = \frac{1}{2}] \frac{7}{2} - \frac{77}{2} = - 35 - 35 = - 35 True Substitute the value y = 5 in the original equation . 14 y^{2} - 77 y = - 35 [Given equation] 14 (5) ² - 77 (5) = - 35 [P u t, y = 5] 350 - 385 - 35 - 35 = - 35 T r u e T h e a n s w e r i s y = 1 / 2, y = 5$

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Solve the following exercise
$14 y^{2} - 77 y = - 35$

Short Answer

Step by step solution

Step 1. given information

Step 2. Simplify the quadratic equation

Step 3. Checking the equation

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Solve the following exercise14y2-77y=-35

Short Answer

Step by step solution

Step 1. given information

Step 2. Simplify the quadratic equation

Step 3. Checking the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Geometry

Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve the following exercise
$14 y^{2} - 77 y = - 35$