Setting = 0 and solving

Quadratic Equations must have 0 on one side of the = before either factoring or using the quadratic formula

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 2B: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring. Check your answer.

x2 + 4x = 21x2 + 4x = 21

–21 –21x2 + 4x – 21 = 0

(x + 7)(x –3) = 0

x + 7 = 0 or x – 3 = 0

x = –7 or x = 3

The solutions are –7 and 3.

The equation must be set = 0. So subtract 21 from both sides.

Factor the trinomial.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Example 2D: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring. Check your answer.–2x2 = 20x + 50

The equation must be written in standard form. So add 2x2 to both sides.

Can divide by 2.

+2x2 +2x2

0 = 2x2 + 20x + 50

–2x2 = 20x + 50

2x2 + 20x + 50 = 0

2(x2 + 10x + 25) = 0

Factor the trinomial.2(x + 5)(x + 5) = 0

2 ≠ 0 or x + 5 = 0

x = –5 Solve the equation.

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Check It Out! Example 2b

Solve the quadratic equation by factoring. Check your answer.

x2 + 4x = 5

x2 + 4x = 5 –5 –5

x2 + 4x – 5 = 0

Write the equation in standard form. Add – 5 to both sides.

Factor the trinomial.

Solve each equation.

(x – 1)(x + 5) = 0

x – 1 = 0 or x + 5 = 0

x = 1 or x = –5

The solutions are 1 and –5.

Holt Algebra 2

5-3 Solving Quadratic Equations by Graphing and Factoring

x2 – 4x = –4

Find the roots of the equation by factoring.

x2 – 4x + 4 = 0

(x – 2)(x – 2) = 0

x – 2 = 0 or x – 2 = 0

x = 2 or x = 2

Rewrite in standard form.

Solve each equation.

Factor

Check It Out! Example 4a

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Check It Out! Example 2c

Solve the quadratic equation by factoring. Check your answer.

30x = –9x2 – 25

–9x2 – 30x – 25 = 0

–1(3x + 5)(3x + 5) = 0

–1(9x2 + 30x + 25) = 0

–1 ≠ 0 or 3x + 5 = 0

Write the equation in standard form.

Factor the trinomial.

Solve the remaining equation.

Divide by -1

Holt Algebra 1

9-6 Solving Quadratic Equations by Factoring

Lesson Quiz: Part I

Solve each quadratic equation by factoring. Check your answer.

x2 – 11x = –24

–4x2 = 16x + 16

•

3, 8

–2

Holt Algebra 1

9-9 The Quadratic Formula and the DiscriminantExample 1B: Using the Quadratic Formula

Solve using the Quadratic Formula.

x2 = x + 20

1x2 + (–1x) + (–20) = 0 Write in standard form. Identify a, b, and c.

Use the quadratic formula.

Simplify.

Substitute 1 for a, –1 for b, and –20 for c.

Holt Algebra 1

9-9 The Quadratic Formula and the Discriminant

Example 1B Continued

Solve using the Quadratic Formula.

x = 5 or x = –4

Simplify.

Write as two equations.

Solve each equation.

x2 = x + 20

Holt Algebra 1

9-9 The Quadratic Formula and the Discriminant

Check It Out! Example 1b

Solve using the Quadratic Formula.

2 – 5x2 = –9x

Write in standard form. Identify a, b, and c.

(–5)x2 + 9x + (2) = 0

Use the Quadratic Formula.

Substitute –5 for a, 9 for b, and 2 for c.

Simplify

Holt Algebra 1

9-9 The Quadratic Formula and the Discriminant

Check It Out! Example 1b Continued

Solve using the Quadratic Formula.

Simplify.

Write as two equations.

Solve each equation.

2 – 5x2 = –9x

x = – or x = 2