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Setting = 0 and solving

Setting = 0 and solving. Quadratic Equations must have 0 on one side of the = before either factoring or using the quadratic formula. x 2 + 4 x = 21. –21 –21. x 2 + 4 x – 21 = 0. x = –7 or x = 3. The solutions are –7 and 3.

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Setting = 0 and solving

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  1. Setting = 0 and solving Quadratic Equations must have 0 on one side of the = before either factoring or using the quadratic formula

  2. x2 + 4x = 21 –21 –21 x2 + 4x – 21 = 0 x = –7 or x =3 The solutions are –7 and 3. Example 2B: Solving Quadratic Equations by Factoring Solve the quadratic equation by factoring. Check your answer. x2 + 4x = 21 The equation must be set = 0. So subtract 21 from both sides. (x + 7)(x –3) = 0 Factor the trinomial. x + 7 = 0 or x – 3 = 0

  3. –2x2 = 20x + 50 +2x2 +2x2 0 = 2x2 + 20x + 50 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. 2x2 + 20x + 50 = 0 Can divide by 2. 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.

  4. x2 + 4x = 5 –5 –5 x2 + 4x – 5 = 0 Check It Out! Example 2b Solve the quadratic equation by factoring. Check your answer. x2 + 4x = 5 Write the equation in standard form. Add – 5 to both sides. (x – 1)(x + 5) = 0 Factor the trinomial. x – 1 = 0 or x + 5 = 0 x = 1 or x = –5 Solve each equation. The solutions are 1 and –5.

  5. Check It Out! Example 4a Find the roots of the equation by factoring. x2 – 4x = –4 x2 – 4x + 4 = 0 Rewrite in standard form. (x – 2)(x – 2) = 0 Factor x – 2 = 0 or x – 2 = 0 x = 2 or x = 2 Solve each equation.

  6. Check It Out! Example 2c Solve the quadratic equation by factoring. Check your answer. 30x = –9x2 – 25 Write the equation in standard form. –9x2 – 30x – 25 = 0 –1(9x2 + 30x + 25) = 0 Divide by -1 –1(3x + 5)(3x + 5) = 0 Factor the trinomial. –1 ≠ 0 or 3x + 5 = 0 Solve the remaining equation.

  7. Lesson Quiz: Part I • Solve each quadratic equation by factoring. Check your answer. • x2 – 11x = –24 • –4x2 = 16x + 16 3, 8 –2

  8. Example 1B: Using the Quadratic Formula Solve using the Quadratic Formula. x2 = x + 20 Write in standard form. Identify a, b, and c. 1x2 + (–1x) + (–20) = 0 Use the quadratic formula. Substitute 1 for a, –1 for b, and –20 for c. Simplify.

  9. Example 1B Continued Solve using the Quadratic Formula. x2 = x + 20 Simplify. Write as two equations. Solve each equation. x = 5 or x = –4

  10. Check It Out! Example 1b Solve using the Quadratic Formula. 2 – 5x2 = –9x (–5)x2 + 9x + (2) = 0 Write in standard form. Identify a, b, and c. Use the Quadratic Formula. Substitute –5 for a, 9 for b, and 2 for c. Simplify

  11. or x = 2 x = – Check It Out! Example 1b Continued Solve using the Quadratic Formula. 2 – 5x2 = –9x Simplify. Write as two equations. Solve each equation.

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