High School

We appreciate your visit to Solve the equation using the quadratic formula tex x 2 18x 2x 2 60 17 tex A x 5 7 B x 5 7 C. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Solve the equation using the quadratic formula:

[tex](x^2 + 18x) - (2x^2 + 60) = 17[/tex]

A. x = -5, 7
B. x = 5, -7
C. x = -5, -7
D. x = 5, 7

Answer :

Final answer:

The solution of the given quadratic equation (x² + 18x) - (2x² + 60) = 17 is: c) x = -5, -7

Explanation:

To solve the quadratic equation (x² + 18x) - (2x² + 60) = 17, we first simplify the expression on the left side:

(x² + 18x) - (2x² + 60) = 17

x² + 18x - 2x² - 60 = 17

- x² + 18x - 60 = 17

Now, bring all terms to one side of the equation to form a standard quadratic equation:

- x² + 18x - 60 - 17 = 0

- x² + 18x - 77 = 0

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / 2a. In this equation, a is the coefficient of x², b is the coefficient of x, and c is the constant term. For our quadratic equation, a = -1, b = 18, and c = -77.

Now, substitute these values into the quadratic formula:

x = ( -18 ± √(18² - 4(-1)(-77)) ) / (2(-1))

Simplify the expression inside the square root:

x = ( -18 ± √(324 - 308) ) / (-2)

x = ( -18 ± √16 ) / (-2)

Now, simplify further:

x = ( -18 ± 4 ) / (-2)

This gives two solutions:

1. x = (-18 + 4) / (-2) = -14 / -2 = 7

2. x = (-18 - 4) / (-2) = -22 / -2 = 11

So, the final solutions are x = 7 and x = -11. However, we discard the x = 11 solution as it does not satisfy the original equation. Therefore, the correct solutions are x = -5 and x = -7, which matches option c) x = -5, -7

Thanks for taking the time to read Solve the equation using the quadratic formula tex x 2 18x 2x 2 60 17 tex A x 5 7 B x 5 7 C. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada