Question

Solve each equation. I don't know this

Answer 1

1.
`(2x - 3)(x + 7) = 0`

`2x^(2) + 14x - 3x - 21 = 0`

`2x^(2) + 11x - 21 = 0`


`x = \frac{-11 +/- \sqrt{11^(2) - 4(2)(-21)}}{2(2)}`


`x = (-11 +/- √(121 + 168))/(4)`


`x = (-11 +/- √(289))/(4)`


`x = (-11 +/- 17)/(4)`


`x = -2.75 +/- 4.25`

`x = -2.75 + 4.25`
`x = -2.75 - 4.25`

`x = 1.5` 
`x = -7`
---------------------------------------------------------------------------------------------------------- 2.
`8x(2x - 5) = 0`

`8x(2x) - 8x(5) = 0`

`16x^(2) - 40x = 0`

`16x^(2) - 4x + 0 = 0`


`x = \frac{-(-40) +/- \sqrt{(-40)^(2) - 4(16)(0)}}{2(16)}`


`x = (40 +/- √(1600 - 0))/(32)`


`x = (40 +/- √(1600))/(32)`


`x = (40 +/- 40)/(32)`


`x = 1.25 +/- 1.25`

`x = 1.25 + 1.25`
`x = 1.25 - 1.25`

`x = 2.5`
`x = 0`
----------------------------------------------------------------------------------------------------------
3.
`x^(2) + 3x - 10 = 0`


`x = \frac{-3 +/- \sqrt{3^(2) - 4(1)(-10)}}{2(1)}`


`x = (-3 +/- √(9 + 40))/(2)`


`x = (-3 +/- √(49))/(2)`


`x = \frac{-3 +/- {7}}{2}`


`x = -1.5 +/- 3.5`

`x = -1.5 + 3.5`
`x = -1.5 - 3.5`

`x = 2`
`x = -5`
----------------------------------------------------------------------------------------------------------
4.
`x^(2) = 13x - 36`

`x^(2) - 13x + 36 = 13x - 13x - 36 + 36`

`x^(2) - 13x + 36 = 0`


`x = \frac{-(-13) +/- \sqrt{(-13)^(2) - 4(1)(36)}}{2(1)}`



`x = (13 +/- √(169 - 144))/(2)`


`x = (13 +/- √(25))/(2)`


`x = (13 +/- 5)/(2)`


`x = 6.5 +/- 2.5`

`x = 6.5 + 2.5`
`x = 6.5 - 2.5`

`x = 9`
`x = 4`
----------------------------------------------------------------------------------------------------------
5.
`3x^(2) - 7x + 2 = 0`


`x = \frac{-(-7) +/- \sqrt{(-7)^(2) - 4(1)(2)}}{2(3)}`


`x = (7 +/- √(49 - 8))/(6)`


`x = (7 +/- √(41))/(6)`


`x = (7 +/- 6.403124237432849)/(6)`


`x = 1.167+/- 1.06718737290547`

`x = 1.67 + 1.06718737290547`
`x = 1.167 - 1.06718737290547`

`x = 2.73718737290547`
`x = 0.60281262709453`
----------------------------------------------------------------------------------------------------------
6.
`10x^(2) - 10x + 9 = 5x^(2) + 4x + 1`

`10x^(2) - 5x^(2) - 10x + 10x + 9 - 1 = 5x^(2) - 5x^(2) + 4x + 10x + 1 - 1`

`5x^(2) + 8 = 14x`

`5x^(2) - 14x + 8 = 14x - 14x`

`5x^(2) - 14x + 8 = 0`


`x = \frac{-(-14) + \sqrt{(-14)^(2) - 4(5)(8)}}{2(5)}`


`x = (14 +/- √(196 - 160))/(10)`


`x = (14 +/- √(36))/(10)`.


`x = (14 +/- 6)/(10)`


`x = 1.4 +/- 0.6`

`x = 1.4 + 0.6`
`x = 1.4 - 0.6`

`x = 2`
`x = 0.8`