XxMassomestbacchixXidn
Answered

Join the IDNLearn.com community and get your questions answered by experts. Find the solutions you need quickly and accurately with help from our knowledgeable community.

completing the square method sucks!!
find the roots of equation by completing the square method
[tex]4x {}^{2} + 3x + 5 = 0[/tex]
​

Sagot :

[tex]\huge\underline\purple{Answer ☘}[/tex]

[tex]4x {}^{2} + 3x + 5 = 0 \\ \\ dividing \: by \: 4... \\ \frac{4x {}^{2} }{4} + \frac{3x}{4} + \frac{5}{4} = 0 \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\ we \: know \: that... \\ \: (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab \\ \\ here... \\ 2ab = \frac{3x}{4} \\ = > 2xb = \frac{3x}{4} \: \: \: \: \: \: \: \: \: (a = x) \\ 2b = \frac{3}{4} \\ b = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} [/tex]

nσw ín σur єquαtíσn...

[tex]x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\adding \: and \: subtracting \: (\frac{3}{8}){}^{2} \\ \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} + ( \frac{3}{8} ) {}^{2} { - ( \frac{3}{8} })^{2} = 0 \\ \\ x {}^{2} + \frac{3x}{4} + (\frac{3}{8} ) {}^{2} + \frac{5}{4} - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} + \frac{5}{4 } - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} = (\frac{3}{8} ) {}^{2} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9}{64} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 5(16)}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 80}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{ - 71}{64} [/tex]

ѕíncє..

ѕquαrє σf αnч numвєr cαn't вє nєgαtívє..

ѕσ.. αnѕwєr dσєѕ nσt єхíѕt~

hσpє hєlpful~

~Be Brainly!

Pstnonsonjokuidn

The roots of the equation are ±71/64i - 3/8.

What is completing the square?

The completing the square method is one of the methods of solving a quadratic equation. Now we have to solve the equation 4x^2 + 3x + 5 = 0 using this method.

First, we must divide through by 4 to have;

x^2 + 3/4x + 5/4 = 0

Next we add half of 3/4 to both sides after taking 5/4 to the RHS

(x + 3/8)^2 = -5/4 + (3/8)^2

(x + 3/8)^2 = -5/4 + 9/64

(x + 3/8)^2 = -80 + 9 /64

(x + 3/8)^2 =-71/64

x = √-71/64 - 3/8

x =  ±71/64i - 3/8

Learn more about completing the square: https://brainly.com/question/2055939