6.1: Choosing a Solving Method | Algebra 1 Honors

How it works

Choose a method based on the equation structure. Factoring works efficiently when integer factors are visible. Isolating a squared expression supports square roots. The quadratic formula works for every quadratic with nonzero leading coefficient; include both signs when taking square roots.

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\quad(a\ne0)

Worked examples

Example 1

Solve $\displaystyle x^2-5x+6=0$ .

Factor: $\displaystyle (x-2)(x-3)=0$ . The zero-product property gives $\displaystyle x=2$ or $\displaystyle x=3$ .

Example 2

Solve $\displaystyle (x-1)^2=9$ .

Take both square-root signs: $\displaystyle x-1=\pm3$ . Therefore $\displaystyle x=4$ or $\displaystyle x=-2$ .

Problems

Problem 6.1.1

Solve $\displaystyle x^2+2x-8=0$ .

Show worked solution

Factor: $\displaystyle (x+4)(x-2)=0$ , giving $\displaystyle x=-4$ or $\displaystyle x=2$ .

Problem 6.1.2

Solve $\displaystyle 2x^2-8=0$ .

Show worked solution

$\displaystyle x^2=4$ , so $\displaystyle x=\pm2$ .

Problem 6.1.3

Solve $\displaystyle x^2-2x-1=0$ exactly.

Show worked solution

Using the quadratic formula gives $\displaystyle x=(2\pm\sqrt{8})/2=1\pm\sqrt{2}$ .

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 6.1.1

Problem 6.1.2

Problem 6.1.3

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