3 Solve the equation 5x2 - 6x - 3 = 0.
Show all your working and give your answers correct to 2 decimal places.

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x²+bx=c.

Add 3 to both sides of the equation.

Subtracting -3 from itself leaves 0.

Subtract -3 from 0.

Divide both sides by 5.

Dividing by 5 undoes the multiplication by 5.

Divide -6 by 5.

Divide -6/5, the coefficient of the x term, by 2 to get -3/5. Then add the square of -3/5 to both sides of the equation. This step makes the left-hand side of the equation a perfect square.

Square -3/5 by squaring both the numerator and the denominator of the fraction.

Add 3/5 to 9/25 by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

Factor . In general, when is a perfect square, it can always be factored as .

Take the square root of both sides of the equation.

Simplify.

Add 3/5 to both sides of the equation.