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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Equations by Factoring

 WHAT TO DO: HOW TO DO IT: 1. Solve the equation x 2 + 4(x+1) 2 = (2x + 3) 2 Remove parentheses and simplify both sides: Rewrite in standard equation form and solve the equation: ⇒ Scratch: Find a numbers whose product is 5 with difference of 4 , larger sign "−". Set each factor equal to zero: The solution: x 2 + 4(x+1) 2 = (2x + 3) 2 x 2 + 4(x 2+2x+1) = 4x 2 + 12x +9 x 2 + 4x 2+8x+4 = 4x 2 + 12x +9 x 2 − 4x − 5 = 0 {5,1}  (x − 5)(x + 1) = 0 (x − 5) = 0 or (x + 1) = 0 x = 5 or x = − 1 Check the original, equation x 2 + 4(x+1) 2 = (2x + 3) 2 ⇒ x = 5 ⇒ x = -1 (5)2 + 4(5+1)2 = (2Â·5+3)2 , 25 + 144 = 139 (-1)2 + 4(-1+1)2 = (2Â·-1+3)2 , 1 + 0 = 1 2. Solve the equation x 3 = 9x 2 − 20x Rewrite in standard equation form and solve the equation: ⇒ Factor out the common factor x ⇒ Scratch: Solve the inner equation: ⇒ Find a pair of numbers whose product is 20 with sum of 9. sign "−". Set each factor equal to zero:  The solution: x 3 = 9x 2 − 20x x 3 − 9x 2 + 20x = 0 x (x 2 − 9x + 20) = 0 x (x 2 − 9x + 20) = 0 x (x − 5)(x − 4) = 0 x = 0, (x − 5) = 0 or (x − 4) = 0 x = 0, x = 4 or x = 3 Check the original equation:  x 3 = 9x 2 − 20x ⇒ x = 0: ⇒ x = 4: ⇒ x = 5 (0)3 = 9(0)2 − 20(0) , 0 = 0 - 0 (4)3 = 9(4)2 − 20(4) , 64 = 144 - 80 (5)3 = 9(5)2 − 20(5) , 125 = 225 - 100