In Exercises 19 to 26, solve each equation by using the Quadratic Formula. Give exact solutions in simplified form. When answers contain square roots, approximate the solutions rounded to two decimal places. x 2 + 9 = 7 x

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To determine To find: To solve each equation by using the Quadratic Formula Explanation Consider the following equation, x 2 + 9 = 7 x . Subtract 7 x on both sides to get the following, x 2 + 9 − 7 x = 7 x − 7 x x 2 − 7 x + 9 = 0 The general form of the quadratic equation is given below, a x 2 + b x + c = 0 Where a is the number multiplied by x 2 , b is the number multiplied by x , and c is the constant term. Quadratic formula: The solution for a x 2 + b x + c = 0 when a ≠ 0 is given below, x = − b ± b 2 − 4 a c 2 a ... ( 1 ) Compare the given equation with general equation to get the following, a x 2 + b x + c = 0 ⇒ x 2 − 7 x + 9 = 0 Therefore, a = 1 , b = − 7 and c = 9 . Since a ≠ 0 . Substitute these values in equation (1) to get the following,

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Elementary Geometry for College St...

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

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BuyFind

Elementary Geometry for College St...

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Solutions

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Section

Answer 3

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Answer 4

Chapter

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Answer 5

To determine

To find:

To solve each equation by using the Quadratic Formula

Explanation of Solution

Consider the following equation,

x2+9=7x.

Subtract 7x on both sides to get the following,

x2+9−7x=7x−7xx2−7x+9=0

The general form of the quadratic equation is given below,

ax2+bx+c=0

Where a is the number multiplied by x2, b is the number multiplied by x, and c is the constant term.

Quadratic formula:

The solution for ax2+bx+c=0 when a≠0 is given below,

x=−b±b2−4ac2a...(1)

Compare the given equation with general equation to get the following,

ax2+bx+c=0⇒x2−7x+9=0

Therefore,

a=1,b=−7 and c=9. Since a≠0.

Substitute these values in equation (1) to get the following,

In Exercises 19 to 26, solve each equation by using the Quadratic Formula. Give exact solutions in simplified form. When answers contain square roots, approximate the solutions rounded to two decimal places. x 2 + 9 = 7 x

Elementary Geometry for College St...

Solutions

Elementary Geometry for College St...

In Exercises 19 to 26, solve each equation by using the Quadratic Formula. Give exact solutions in simplified form. When answers contain square roots, approximate the solutions rounded to two decimal places.

x 2 + 9 = 7 x

Explanation of Solution

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