How can I do this?
x(4x-7)= -3
2007-01-26 03:33:32 · 8 answers · asked by Rayados Monterrey 2 in Science & Mathematics ➔ Mathematics
Please specify what needs to be done, what needs to be solved. I assume you need to solve for "x," correct?
First: eliminate parenthesis > use distribution by multiplying the outer term with the terms in parenthesis...
x(4x) + x(7) = -3
4x^2 + 7x = - 3
Sec: set the equation to "0" > add "3" to both sides (When you move a variable to the opposite side, always use the opposite sign)....
4x^2 + 7x + 3 = - 3 + 3
4x^2 + 7x + 3 = 0
Third: factor > multiply the 1st and 3rd coefficient to get "12." Find two numbers that give you "12" when multiplied and "7" (2nd/middle coefficient) when added/subtracted. The numbers are: "4 and 3"....
*Rewrite the expression including the new middle coefficients....
4x^2 + 4x + 3x + 3 = 0
*When you have 4 terms - group "like" terms and factor....
(4x^2 + 4x) + (3x + 3) = 0
4x(x + 1) + 3(x + 1) = 0
(x + 1)(4x + 3) = 0
Fourth: solve the two x-variables > set both parenthesis to "0"....
a. x + 1 = 0
x + 1 - 1 = 0 - 1
x = -1
b. 4x + 3 = 0
4x + 3 - 3 = 0 - 3
4x = - 3
4x/4 = -3/4
x = -3/4
Solutions: -3 and -3/4
2007-01-26 05:18:47 · answer #1 · answered by ♪♥Annie♥♪ 6 · 0⤊ 0⤋
Expand it first:
x*4x - x*7=-3
4x^2 -7x =-3
4x^2-7x+3=0
Solve this by using the formula for cuadratic equations:
x = (7 +- sqrt( 7^2-4*4*3))/(2*4)
x = (7 +- sqrt( 49 - 48) )/8
x = (7 +- sqrt( 1) ) /8
x = (7+-1)/8
x1= 1
x2=3/4
2007-01-26 11:45:33 · answer #2 · answered by krumenager 3 · 1⤊ 1⤋
* first expand..
4x^2 - 7x = -3
*transpose -3,
4x^2 - 7x + 3 = 0
*factor out
(x - 1) (4x - 3) = 0
therefore,
(i)
(x-1) = 0
x = 1
(ii)
4x - 3 =
4x = 3
x = 3/4
answer: X = 1 or 3/4
:0<
2007-01-26 11:47:13 · answer #3 · answered by swas77 2 · 0⤊ 1⤋
first we multiply it out...
4x^2 - 7x = -3
Now we solve for 0...
4x^2 - 7x + 3 = 0
Now we can solve for x using the quadratic formula!
x = [-b +/- (b^2 - 4ac)^.5] / 2a where a = 4, b = -7, and c = 3
x = [7 +/- (49 - 4*4*3)^.5] / 8
x = [7 +/- (1)^.5) / 8
x = (7 +/- 1) / 8 = 8/8 and 6/8
x = 1 or .75
Hope this helps! :)
2007-01-26 11:41:57 · answer #4 · answered by disposable_hero_too 6 · 1⤊ 2⤋
x(4x-7) = -3
4x^2-7x = -3
4x^2-7x+3=0
(4x-3)(x-1)=0
x = 1 or 3/4
2007-01-26 12:01:26 · answer #5 · answered by Kyrix 6 · 0⤊ 2⤋
Distribute the X.
4(x^2)-7x=-3
Add 3 to both sides.
4(x^2)-7x+3=0
Now use the quadratic formula.
a=4
b=-7
c=3
Plug them in.
2007-01-26 11:43:32 · answer #6 · answered by Anonymous · 1⤊ 1⤋
4x^2-7x+3=0
4x^2-4x-3x+3=0
4x(x-1)-3(x-1)=0
(4x-3)(x-1)=0
therefore x=3/4 or 1
2007-01-26 11:42:13 · answer #7 · answered by SS 2 · 1⤊ 2⤋
4x^2-7x+3=0
4x^2-4x-3x+3=0
4x(x-1)-3(x-1)=0
(4x-3)(x-1)=0
x=3/4 or 1
2007-01-26 12:07:26 · answer #8 · answered by avant1991 3 · 0⤊ 1⤋