29 Mar

Solving quadratic equations by completing the square method is important and understanding it helps a lot.

Completing the square ${\left(x+a\right)}^{2}={x}^{2}+2\mathrm{ax}+{a}^{2}$ is the process of rearranging one side of a quadratic equation into a perfect square before solving and is achieved by following these simple rules:

## Problem 1

Solve this equation using completing the square

## $\huge&space;2x^2+5x+3=0{\color{Magenta}&space;}$

LHS = RHS

1. Begin with a quadratic equation in monic standard form  $a{x}^{2}+\mathrm{bx}+c$ , otherwise, simplify the equation until the coefficient of x2 is reduced to unity.

2. Divide each side by a, the coefficient of the squared term.

3. Subtract the constant terms from both sides of the equation

4. Rearrange the equations so that the x2 and x terms are on one side of the equals sign and the constant is on the other side.

5. Add the square of one-half of

$\frac{c}{a}$

, the coefficient of x, to both sides and make it the left side into a perfect square.

6. Evaluate the left side as square and simplify the right hand side where necessary.

7. Take the square root of both sides of the equation (remembering that the square root of a number gives a ± answer).

8. Solve the two linear equations with respect to ±