Aim: How Do We Solve Quadratic Equations by Factoring Do Now: Factor: x 2 + 3x –18.

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Presentation transcript:

Aim: How Do We Solve Quadratic Equations by Factoring Do Now: Factor: x 2 + 3x –18

Example: Solve. x 2 +3x-18=0 x 2 +3x-18=0Factor the left side (x+6)(x-3)=0set each factor =0 x+6=0 OR x-3=0solve each eqn x=-6 OR x=3check your solutions!

Example: Solve. 2t 2 -17t+45=3t-5 2t 2 -17t+45=3t-5Set eqn. =0 2t 2 -20t+50=0factor out GCF of 2 2(t 2 -10t+25)=0divide by 2 t 2 -10t+25=0factor left side (t-5) 2 =0set factors =0 t-5=0solve for t +5 t=5check your solution!

Example: Solve. 3x-6=x x-6=x 2 -10Set = 0 0=x 2 -3x-4Factor the right side 0=(x-4)(x+1)Set each factor =0 x-4=0 OR x+1=0 Solve each eqn x=4 OR x=-1 Check your solutions!

Solve for x: 3 + x 2 – x = 5 x 2 – x – 2 = 0 (x – 2)(x + 1) = 0 x = 2, x = –1

Solve for x: 2x 2 + 4x = 30 2(x 2 + 2x – 15) = 0 x 2 + 2x – 15 = 0 (x + 5)(x - 3) = 0 x = -5, x = 3

Solve x 2 – 5x = 0. x(x – 5) = 0 x = 0, x = 5 Solve (x – 5) 2 – 100 = 0. The left side of the equation is the difference of two squares, then factor it into two binomials [(x – 5) + 10][(x – 5) – 10] = 0 (x +5)(x – 15) = 0 x = -5, x = 15

Solve for x: 2x 2 – 4x = 12 + x 2x 2 – 5x – 12 = 0 (2x + 3)(x – 4) = 0 2x + 3 = 0, x – 4 = 0 x = 4

You Try It! Solve the following equations: 1.x 2 – 25 = 0 2.x 2 + 7x – 8 = 0 3.x 2 – 12x + 36 = 0 4.c 2 – 8c = 0 5.5b b 2 = 7b