Question

What are the approximate solutions of 2x2 + 9x = 8 to the nearest hundredth?

Answer 1

`2x^(2)` + 9x = 8 Subtract 8 from both sides

`2x^(2)` + 9x -8 = 0 Plug these into the Quadratic Formula

a = 2 , b = 9 , c = -8

x =
`\frac-{b (+ or -) \sqrt{ b^(2) - 4ac} }{2a}` Plug in the values
x =
`\frac{-9 (+ or -) \sqrt{ 9^(2)-4(2)(-8) } }{2(2)}` Multiply 2 and 2
x =
`\frac{-9 (+ or -) \sqrt{ 9^(2)-4(2)(-8) } }{4}` Multiply -4 and 2
x =
`\frac{-9 (+ or -) \sqrt{ 9^(2)-8(-8) } }{4}` Multiply -8 and -8
x =
`\frac{-9 (+ or -) \sqrt{ 9^(2)+64} }{4}` Square 9
x =
`(-9 (+ or -) √(81 + 64) )/(4)` Add 81 and 64
x =
`(-9 (+ or -) √(145) )/(4)` Take apart the (+ or -)
x =
`(-9 + √(145) )/(4)` and
`(-9 - √(145) )/(4)` Find the square root of 145
x ≈
`(-9 +12.0415945788)/(4)` or
`(-9 -12.0415945788 )/(4)` Add -9 and the decimal , Subtract -9 and the decimal
x ≈
`(3.0415945788)/(4)` or
`(-21.0415945788)/(4)` Divide both fractions
x ≈ 0.7603986447 or -5.2603986447 Round to the nearest hundredth (_._x)
x ≈ 0.76 or -5.26