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Solve by completing the square

5x^(2)+3x-4=0

Solve by completing the square $\newline$ $5 x^{2}+3 x-4=0$

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Solve complex trigonomentric equations

Full solution

Q. Solve by completing the square

\newline

5 x^{2}+3 x-4=0

Divide by $5$ : First, divide the equation by $5$ to make the coefficient of $x^2$ equal to $1$ . $\newline$ $5x^2 + 3x - 4 = 0$ $\newline$ $x^2 + \left(\frac{3}{5}\right)x - \frac{4}{5} = 0$
Move constant term: Next, move the constant term to the other side of the equation. $x^2 + \left(\frac{3}{5}\right)x = \frac{4}{5}$
Complete the square: Now, to complete the square, add $(\frac{b}{2})^2$ to both sides, where $b$ is the coefficient of $x$ . $\frac{3}{5}/2 = \frac{3}{10}$ $\left(\frac{3}{10}\right)^2 = \frac{9}{100}$ $x^2 + \left(\frac{3}{5}\right)x + \frac{9}{100} = \frac{4}{5} + \frac{9}{100}$
Add fractions: Find a common denominator and add the fractions on the right side. $\newline$ $x^2 + \frac{3}{5}x + \frac{9}{100} = \frac{80}{100} + \frac{9}{100}$ $\newline$ $x^2 + \frac{3}{5}x + \frac{9}{100} = \frac{89}{100}$
Write as trinomial: Write the left side as a perfect square trinomial. $\newline$ $(x + \frac{3}{10})^2 = \frac{89}{100}$
Take square root: Take the square root of both sides. $\newline$ $x + \frac{3}{10} = \pm\sqrt{\frac{89}{100}}$ $\newline$ $x + \frac{3}{10} = \pm\frac{\sqrt{89}}{10}$
Subtract $\frac{3}{10}$ : Subtract $\frac{3}{10}$ from both sides to solve for $x$ . $x = -\frac{3}{10} \pm \frac{\sqrt{89}}{10}$
Simplify expression: Simplify the expression. $x = \frac{{-3 \pm \sqrt{89}}}{{10}}$

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