2007-01-25 16:12:20 · 8 answers · asked by savannah_banana03 1 in Science & Mathematics ➔ Mathematics
First: set the equation to "0" > subtract "13x" from both sides...
4x^2 - 13x = 13x - 13x + 12
4x^2 - 13x = 12
*Subtract "12" to both sides...
4x^2 - 13x - 12 = 12 - 12
4x^2 - 13x - 12 = 0
Sec: factor...multiply the 1st and 3rd cofficient to get "-48" when multiplied and "-13" (2nd/middle coefficient) when added/subtracted. The numbers are: "-16 and 3".....
*Rewrite the equation with the new middle cofficients....
4x^2 - 16x + 3x - 12 = 0
*When you have 4 terms - group "like" terms and factor...
(4x^2 - 16x) + (3x - 12) = 0
4x(x - 4) + 3(x - 4) = 0
(x - 4)(4x + 3) = 0
Third: solve for the x-variables > set both parenthesis to equal "0"
a. x - 4 = 0
x - 4 + 4 = 0 + 4
x = 4
b. 4x + 3 = 0
4x + 3 - 3 = 0 - 3
4x = - 3
4x/4 = -3/4
x = -3/4
Solutions: 4 and -3/4
2007-01-25 16:24:23 · answer #1 · answered by ♪♥Annie♥♪ 6 · 1⤊ 0⤋
the basic thanks to unravel any quadratic equation is the quadratic formula. merely placed each and every of the equations contained in the type: ax^2 + bx + c and then use the formula: x = [-b +- sqrt(b^2 -4ac)] / 2a So: a million) x^2 + 7x + 10 = 0 that's already contained in the right type, so: a =a million, b =7, c =10 x = [-7 +- sqrt(40 9 - 4(a million)(10))] / 2(a million) = [-7 +- sqrt(9)] / 2 = [-7 +- 3] / 2 So: x = (-7 + 3) / 2 = -2 x = (-7 - 3) / 2 = -5 you may also merely attempt to imagine out the topic matters. This one is trouble-free because 5 and a pair of upload as a lot as 7 and multiply to 10, so x^2 +7x + 10 = (x + 5)(x + 2) = 0 Set both equivalent to 0 and settle on. x + 5 = 0 => x = -5 x + 2 = 0 => x = -2 So there are 2 strategies to unravel quadratics. settle on each and every of the topic matters like that, and for the topic matters like 5), 6), and 9), flow each and every of the words to at least one area with the different area equivalent to 0 so that you would use the quadratic formula.
2016-12-03 01:43:27 · answer #2 · answered by lesure 4 · 0⤊ 0⤋
4x^2 - 13x - 12 = 0
rewriting the equation with the new middle cofficients....
4x^2 - 16x + 3x - 12 = 0
(4x^2 - 16x) + (3x - 12) = 0
4x(x - 4) + 3(x - 4) = 0
(x - 4)(4x + 3) = 0
either x - 4 = 0 => x = 4
or 4x + 3 = 0 =>4x = - 3
x = -3/4
hence x= 4 , -3/4
2007-01-25 16:45:50 · answer #3 · answered by rajeev_iit2 3 · 1⤊ 0⤋
You use the quadratic formula to solve this one but first you must get it in standard form which is ax^2 + bx + c = 0
-4x^2 +13x + 12 = 0
Quadratic formula is x = -b + or - sqr(b^2 - 4ac)/2a
x will have 2 values
sqr = square root
2007-01-25 16:25:27 · answer #4 · answered by ikeman32 6 · 0⤊ 0⤋
Subtract 13x and 12 from both sides:
4x^2-13x-12=0
(4x+3)(x-4)=0
4x+3=0
x-4=0
x=-3/4 and 4
2007-01-25 17:02:48 · answer #5 · answered by Anonymous · 0⤊ 0⤋
4x^2=13x+12
4x^2 - 13x - 12 = 0
so, you need two numbers that multiply to (-12)(4) = -48 and add to -13...-16 and 3
0 = 4x^2 - 16x + 3x -12
0 = 4x(x - 4) + 3(x - 4)
0 = (4x + 3)(x - 4)
x - 4 = 0
x = 4
4x + 3 = 0
x = -(3/4)
2007-01-25 16:22:04 · answer #6 · answered by Anonymous · 1⤊ 0⤋
4x^2 -13x -12=0
4x^2 -16x+3x-12=0
(4x+1)(3x-12)=0
=>x= -1/4 , 4
2007-01-25 16:21:20 · answer #7 · answered by Mohammed S 2 · 0⤊ 1⤋
It can't be factored. Use the quadratic equation.
http://mathworld.wolfram.com/QuadraticEquation.html
2007-01-25 16:21:46 · answer #8 · answered by Singh 2 · 0⤊ 0⤋