# Solving Quadratic Equations Using Square Roots & Completing the Square

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Solving Quadratic Equations Using Square Roots & Completing the Square

Using Square Roots to Solve a Quadratic Equation
When a quadratic equation is in the form , it can be solved by isolating the Quadratic term and using square roots. Stress the fact that by definition, the square root of x2 = the absolute value of x. You may also need to remind students that the absolute value of x, is the distance away from zero. Point out that this method of isolating the quadratic and taking the square root of both sides is only possible because there is no linear term.

Solve Using Square Roots
Other Method:

Solve Using Square Roots
Stress to students that answers should be left exact unless otherwise stated.

Solve Using Square Roots
Stress to students that answers should be left exact unless otherwise stated.

Solve Using Square Roots
The square root of a negative number is undefined in the set of real numbers. What would happen if you graph this quadratic: The parabola would not have any x intercepts.

Solve Using Square Roots
Since this quadratic has only one solution, the vertex of the related parabola is on the x axis, therefore only one x intercept.

Solve Using Square Roots

Solve Using Square Roots
Perfect Square Trinomial Binomial Square Can we solve this quadratic using a different method? Students will need to recall that a perfect square trinomial factors into a binomial square. This example will help lead into completing the square.

Solve by Factoring

We will Use a method called Completing the Square to solve.
Solve by Factoring We will Use a method called Completing the Square to solve.

Solve by Completing the Square
NOT a Perfect Square Trinomial Move the constant to the other side. 2. Add the square of half the linear coefficient to both sides. Factor the perfect square trinomial into a binomial square.

Solve by Completing the Square
NOT a Perfect Square Trinomial Move the constant to the other side. 2. Add the square of half the linear coefficient to both sides. Factor the perfect square trinomial into a binomial square.

Solve by Completing the Square
NOT a Perfect Square Trinomial Move the constant to the other side. 2. Add the square of half the linear coefficient to both sides. Factor the perfect square trinomial into a binomial square.

Solve by Completing the Square
Divide both sides by leading coefficient. Move the constant to the other side. 2. Add the square of half the linear coefficient to both sides. Factor the perfect square trinomial into a binomial square.