Since we are solving for m and it is in the denominator, multiply both sides by m to eliminate the denominator. m v2 300VP Multiply both sides by m. m 300VP v2 Divide both sides by v2. YOU TRY 1 Solve v A 2E m for m. We may need to use the quadratic formula to solve a formula for a variable. Compare the following equations. Each equation is quadratic in x because each is written in the form ax2 bx c 0. 8x2 3x 2 0 and 8x2 tx z 0 a 8 b 3 c 2 a 8 b t c z To solve the equations for x, we can use the quadratic formula. EXAMPLE 2 Solve for x. a) 8x2 3x 2 0 b) 8x2 tx z 0 Solution a) 8x2 3x 2 does not factor, so we will solve using the quadratic formula. 8x2 3x 2 0 a 8 b 3 c 2 x 3 2(3)2 4(8)(2) 2(8) 3 19 64 16 3 173 16 The solution set is e3 173 16 , 3 173 16 f . b) Solve 8x2 tx z 0 for x using the quadratic formula. a 8 b t c z x 2 4(8)(z) 2(8) t 2t x b 2b2 4ac 2a t 2t2 32z 16 Perform the operations. The solution set is et 2t2 32z 16 , t 2t2 32z 16 f . YOU TRY 2 Solve for n. a) 3n2 5n 1 0 b) 3n2 pn r 0 646 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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