Can You Use The Quadratic Formula To Solve These Equations And Show Your Work?

[ Stands For Square Root. Standard Form Is Ax^2+bx+c=0. Quadratic Formula Is X=-b+or-[(b^2-4ac) / 2a. In standard form x^2-16x+7=0 6u^2+4u+11=0 not in standard form x^2+6x=-15 7x-5+12x^2=-3x solve these using the quadratic formula and by factoring to check your solutions z^2+15z+24=-32 r^2-4r+8=5r 9n^2-42n-162=21n

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Student850

asked 1 year ago

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Here's one of each.

Standard Form
6u² + 4u + 11 = 0    (a=6, b=4, c=11)
u = (-4±√(4² - 4*6*11))/(2*6) = (-4±√(16-264))/12
  = (-4±√(-4*62))/12
u = (-1/3) ± i(1/6)√62

Non-standard Form
7x - 5 + 12x² = -3x
12x² + 10x - 5 = 0    (add 3x to both sides; a=12, b=10, c=-5)
x = (-10±√(10² - 4*12*(-5)))/(2*12) = (-10±√(100+240))/24
  = (-10±√340)/24 = (-10±√(4*85))/24
x = (-5±√85)/12

Factor, too
z² + 15z + 24 = -32
z² + 15z + 56 = 0    (add 32 to both sides; a=1, b=15, c=56)
z = (-15±√(152-4*1*56))/(2*1) = (-15±√(225-224))/2
z = -16/2  or -14/2
z = -8  or  -7

z² + 15z + 56 = (z+8)(z+7) = 0
z = -8  or  -7    (this compares with the values obtained from the formula)