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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 326. (page 1240)

Solve the quadratic equations below. Use any method you want.
$8 v^{2} + 3 = 35$

Short Answer

Expert verified

As a result, the two solutions are $v = - \frac{\sqrt{66}}{4}$ and $v = - \frac{\sqrt{66}}{4}$

Step by step solution

01

Given information.

The given equation is $8 v^{2} + 3 = 35$

02

Step 2. Use the quadratic formula to solve the equation.

First, write the equation $a x^{2} + b x + c$ in standard form, as shown below.

First both side subtract by 35

$8 v^{2} + 3 = 35 8 v^{2} + 3 - 35 = 35 - 35 8 v^{2} - 33 = 0$

This is already done in this place.

Determine the a, b, and c values.

When compared to the standard, the values are a = 8 b = 0 and c= -33.

In the quadratic formula, substitute a=8,b=0, and c= -33.

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

role="math" localid="1653846596213" $b = \frac{0 卤 \sqrt{{(0)}^{2} - 4 (8) (- 33)}}{2 (8)}$

As shown below, simplify the fraction.

$b = \frac{0 卤 \sqrt{{(0)}^{2} - 4 (8) (- 33)}}{2 (8)} b = \frac{卤 \sqrt{1056}}{4} b = \frac{卤 4 \sqrt{66}}{16} b = \frac{卤 \sqrt{66}}{4}$

As a result, the two solutions are $v = - \frac{\sqrt{66}}{4}$ and role="math" localid="1653847043221" $v = - \frac{\sqrt{66}}{4}$

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