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

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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

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