algebra lesson cumulative

Question

rewrite each equation so that the espression on one side could be graphed and the x intercepts of the graph would show the solution to the equation.

a. 3x^2=81

b. (x-1)(x+1)-9=5x

c. x^2-9x+10=32

d.6x(x-8)=29

Answer 1

3x^2-81 =0

x^2 - 27= 0

x = + or - square root of 27 = +3sqr3

(x^2-1)-9 -5x =0

x^2 -5x -10 = 0

x = about 2.5 + 4 = -1.5, 6.5, or very close to that.

x^2-9x +10 =32

x^2 -9x -22 =0

(x-11)(x+2) = 0

x = -2, 11

6x^2 -48x -29= 0

x^2 -8x = 29/6

x^2 -8x + 16 = 29/6 +16

(x-4)^2 = 125/16

x-4 = 5/4sqr5

x = 4 + or - (5/4)2.2

x = 4 + 2.7 = 1.3, 6.7

Answer 2

For these equations, we should rearrange so that the left hand side = 0 (because y = 0, the x axis). I'll simplify too.

(a) 3x² = 81

=> 3x² - 81 = 0

=> 3(x² - 27) = 0

(b) (x - 1)(x + 1) - 9 = 5x

=> x² - 1 - 9 - 5x = 0

=> x² - 5x - 10 = 0

(c) x² - 9x + 10 = 32

=> x² - 9x - 22 = 0 or, the factorized version, if you prefer (x + 2)(x - 11) = 0

(d) 6x(x - 8) = 29

=> 6x² - 48x - 29 = 0

You can graph on Desmos Graphing or similar to see the roots.

https://www.desmos.com/calculator/q6w6m2b1cg

which shows x intercepts at:

(a) (-5.196, 0) & (5.196, 0)

(b) (-1.531, 0) & (6.531, 0)

(c) (-2, 0) & (11, 0)

(d) (-0.564, 0) & (8.564, 0)