Chapter A.5, Problem 25E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# 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. 5 x 2 = 3 x + 7

To determine

To find:

To solve each equation by using the Quadratic Formula

Explanation

Consider the following equation,

5x2=3x+7

Subtract 3x+7 on both sides to get the following,

5x2âˆ’3xâˆ’7=3x+7âˆ’3xâˆ’75x2âˆ’3xâˆ’7=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.

The solution for ax2+bx+c=0 when aâ‰ 0 is given below,

x=âˆ’bÂ±b2âˆ’4ac2a...(1)

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

ax2+bx+c=0â‡’5x2âˆ’3xâˆ’7=0

Therefore,

a=5,b=âˆ’3Â andÂ c=âˆ’7. Since aâ‰ 0.

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

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