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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 10: Q 223 (page 1235)

Solve quadratic equation using the square root property: $5 c^{2} + 3 = 19$

Short Answer

Expert verified

The required result is $c = \pm \frac{4}{\sqrt{5}}$

Step by step solution

01

Given information

The given expression is $5 c^{2} + 3 = 19$

02

Simplifying the equation

Subtract 3 from both side equation

$5 c^{2} = 16$

Divide by 5

$c^{2} = \frac{16}{5}$

03

Square root property

If $x^{2} = k$ and $k \geq 0$ then , $x = \pm k$

$\frac{16}{5} \geq 0$

$c = \pm \sqrt{\frac{16}{5}}$

$c = \pm \frac{4}{\sqrt{5}}$

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Most popular questions from this chapter

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$p^{2} + \frac{1}{4} p$

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$n^{2} + 13 n$

Solve $3 t^{2} + 6 = 70$ .

Solve $16 n^{2} + 40 n + 25 = 4$ .

Solve the quadratic equation using square root property.

$\frac{3}{2} b^{2} - 7 = 41$ .

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