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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 153 (page 899)

Solving quadratic equations $x^{2} + 10 x = 120$ .
(a) by completing the square
(b) using the Quadratic Formula
(c) Which method do you prefer? Why?

Short Answer

Expert verified

The solutions of the equation

(a) by completing the square $\sqrt{145} + 5 and - \sqrt{145} - 5$ .

(b) using the Quadratic Formula $\sqrt{145} + 5 and - \sqrt{145} - 5$

(c) Quadratic Formula.

Step by step solution

01

Step 1. Given information.

The given Quadratic equation is $x^{2} + 10 x = 120$ .

02

Part (a) Step 1. Factor the perfect square trinomial.

$x^{2} + 10 x = 120 x^{2} + 10 x + 25 = 120 + 25 {(x + 5)}^{2} = 145 x + 5 = 卤 \sqrt{145}$

Solve for x:

$x = \sqrt{145} - 5$ and $x = - \sqrt{145} - 5$

03

Part (b) Step 1. Using the Quadratic Formula.

$x^{2} + 10 x = 120$

Subtract 120 to get the equation in standard form.

$x^{2} + 10 x - 120 = 0$

Identify the values of a, b, and c.

$a = 1, b = 10, c = - 120$

Write the quadratic formula. 10

$y = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

Then substitute in the values of a, b, and c.

$y = \frac{- 10 卤 \sqrt{10^{2} - 4 路 1 路 (- 120)}}{2 路 1} y = \frac{- 10 卤 \sqrt{100 + 480}}{2} y = \frac{- 10 卤 \sqrt{580}}{2} y = \frac{- 10 卤 2 \sqrt{145}}{2} y = - 5 卤 \sqrt{145} y = - 5 + \sqrt{145} and y = - 5 - \sqrt{145}$

04

Part (c) Step 1. Quadratic formula.

I prefer the quadratic formula because it it easy to use to finding the roots of the equations.

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