Solving a Quadratic Equation by Completing the Square Method, Solving a Quadratic Equation by Formula Method

**Solving a Quadratic
Equation by Completing the Square Method**

In deriving the formula
for the roots of a quadratic equation we used completing the squares method.
The same technique can be applied in solving any given quadratic equation
through the following steps

**Step 1 **Write the quadratic equation in
general form *ax*^{2} + *bx* +*c* = 0 .

**Step 2 **Divide both sides of the equation
by the coefficient of *x*^{2}
if it is not 1.

**Step 3 **Shift the constant term to the
right hand side.

**Step 4 **Add the square of one-half of the
coefficient of *x* to both sides.

**Step 5 **Write the left hand side as a
square and simplify the right hand side.

**Step 6 **Take the square root on both
sides and solve for *x*.

Solve** ***x*^{2}** **−** **3*x*** **−** **2** **=** **0

x^{2} − 3x − 2 = 0

x^{2} - 3x = 2 (Shifting the
Constant to RHS)

Solve 2*x* ^{2}
− *x* −1 = 0

** Solution **2

Tags : Example, Solution | Algebra Example, Solution | Algebra

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