When a Is Not 1

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 7 of 48.

Completing the square needs ${x}^{2}$ with no number in front. So when a is not 1, divide every term by a first. Dividing both sides by the same number, not 0, keeps the same solutions.

$2{x}^{2}-4x-6 = 0$

Divide every term by 2: ${x}^{2}-2x-3 = 0$ . Completing the square gives ${\left(x-1\right)}^{2} = 4$ . So x = 3 or x = -1.

Challenge

Solve $3{x}^{2}+12x-15 = 0$ by completing the square. Write each line yourself.

Try it yourself

3x^{2}+12x-15 = 0

Get $x$ alone

All lessons in Quadratics & Complex Numbers

1The Vertex

The Axis of Symmetry Drawing from Standard Form Maximum or Minimum Recap: The Vertex

4Imaginary Numbers

Meet i Roots of Negatives Not a Perfect Square Powers of i Recap: Imaginary Numbers

7The Discriminant

Computing It Three Kinds of Answers Reading the Sign Recap: The Discriminant

10Final Challenges

Final: Square It Away Final: The Peak Final: Divide It Final: No Real Roots Final: Where They Meet

2Completing the Square

The Missing Number Completing the SquareWhen a Is Not 1Recap: Completing the Square

5Complex Arithmetic

Adding and Subtracting Multiplying The Conjugate Dividing A Pure Imaginary Bottom Recap: Complex Arithmetic

8Lines Meet Parabolas

Two Crossings Just Touching No Meeting A Circle and a Line Recap: Lines and Parabolas

3Vertex Form by Algebra

From Standard to Vertex Odd Middle Terms A Leading Number Opening Down Recap: Vertex Form

6Complex Solutions

Squares Equal to Negatives A Shifted Square The Formula Goes Complex Fractions in the Answer Recap: Complex Solutions

9Quadratic Models

The Highest Point Back to the Ground The Biggest Area Price and Revenue Recap: Models