Algebra Demystified 2nd Ed
366 alGEbra De mystif ieD The quadratic formula can be messy to compute when any of a, b, or c is a fraction or decimal. We can ...
Chapter 10 QuadratiC EQuations 367 Simplifying this expression is much easier than the expression containing all of the fraction ...
368 alGEbra De mystif ieD PRACTICE Simplify the fraction. 1.^612 2 ± = 2.^1227 6 ± = 3.^248 4 ± = 4.^20300 10 ± = −± − (^620) ...
Chapter 10 QuadratiC EQuations 369 EXAMPLES Solve the quadratic equation with the quadratic formula. 2 x^2 + 3 x+ 1 = 0 We begin ...
370 alGEbra De mystif ieD Solve the quadratic equation with the quadratic formula. 1 3 xx^2 +−= 20 We begin by multiplying both ...
Chapter 10 QuadratiC EQuations 371 2x^2 = 9 –3x^2 + 4x + 1 = 0 9x^2 – x = 10 10x^2 – 5x = 0 01 ..xx^2 – 0111 – = 0 9.^1 3 ...
372 alGEbra De mystif ieD or ()(0) 3 ()^2 ( −− ++=− −−= =−− ±−− 13 411 410 444 2 2 xx xx x ()^33141612 6 428 6 447 6 427 6 2 )( ...
Chapter 10 QuadratiC EQuations 373 80 16 32 0 1 16 80 16 32 2 2 xx xx −−= ()−−=^1 16 (0) 5 () () ()() () xx^2 x −−= =−− ±−−−= ...
374 alGEbra De mystif ieD EXAMPLES Solve the equation. x xx − −− (^1) =− 28 2 (^25) This is in the form “fraction = fraction” so ...
Chapter 10 QuadratiC EQuations 375 Solve the equation. 3 4 624 x^228 x − xx = −+ −− We begin with cross-multiplication. 32 ()xx^ ...
376 alGEbra De mystif ieD 4.^21 1 3 2 87 (^22) x x x x x xx − − − = −− −− 5.^41 1 5 1 x 24 x x xx + − + − − = 6.^2 1 32 2 x xx ...
Chapter 10 QuadratiC EQuations 377 x xx xx x xx x − + = − −−=+ −+=+ 1 23 6 2 1262 3 (^2321218) ()()() ()() −−−− −−= −+= 12 18 ...
378 alGEbra De mystif ieD 4.^21 1 3 2 87 2 2 2 x x x x x xx x − + − − = −− −− Denominatorfactored: −− + − − = −− −+ =+ − + 1 1 3 ...
Chapter 10 QuadratiC EQuations 379 4524 24 3624 24 22 2 xxxxx xxx +− +=− +=− −−+−+ −+= −+= 24 24 24 24 318240 1 3 31824 1 3 2 2 ...
380 alGEbra De mystif ieD 7.^2 21 334 3 32 1 32 1 2 21 3 x xx x x xx xx x x x + −=−− =+ +⋅ + − LCD() () (()^332 ()21 1 34 3 x x ...
Chapter 10 QuadratiC EQuations 381 9.^142133343 1 xxx^2 x xx x − + + − + = − −− Denominatorfactored: −− + + − + = − −+ =− ++ 4 2 ...
382 alGEbra De mystif ieD 13 14 10 13 110 13 10 10 xx^2 xx xx ++= ++= += += ()() −− 11 −− 11 13 x==− =− 11 xxButl=− 1 eads ...
Chapter 10 QuadratiC EQuations 383 Quiz If ( xx– 89 )( )+ = 0 , then a. x=89, b. x=− −89, C. x=−89, d. x=−89, To apply th ...
384 alGEbra De mystif ieD If xx^2 + 91 + 80 = , then a. x=36, b. x=− −36, C. x=29, d. x=− −29, If 32 xx^2 – – 20 = , ...
Chapter 10 QuadratiC EQuations 385 If xxx^ + + 31 + ^282 – 9 = x 6 – 3 , then a. x=26, b. x=71, C. x=± 229 d. there is n ...
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