Question

Solve 5x^2 + 3x - 4 = 0 by completing the square.

Answer 1

So we know that:
\[(a+b)^{2}=a ^{2}+2ab+b ^{2}\]
Now, looking at the problem,.
We need to find a number that can help us complete the formula.

Answer 2

\[5(x^{2}+\frac{3}{5}x) = 4\]
\[x^{2}+\frac{3}{5}x = \frac{4}{5}\]
\[x^{2}+\frac{3}{5}x +(\frac{3}{10})^{2} = \frac{4}{5}+(\frac{3}{10})^{2}\]
\[(x+\frac{3}{10})^{2} = \frac{4}{5}+\frac{9}{100}\]
\[(x+\frac{3}{10})^{2} = \frac{89}{100}\]
\[x + \frac{3}{10} = \frac{\pm \sqrt{89}}{10}\]
\[x = \frac{-3 \pm \sqrt{89}}{10}\]

Answer 3

thank you guys