Equation Provide 2 methods to solve the equation x^2 + 3x – 4 = 0?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
Another method to solve x^2 + 3x – 4 = 0 is by factorization.
x^2 + 3x – 4 = 0
=> x^2 + 4x - x - 4 = 0
=> x( x + 4) - 1(x + 4) = 0
=> (x - 1)(x + 4) = 0
=> x = 1 and x = -4
The solution of the equation is x = 1 and x = -4
Related Questions
- Equation .Solve the equation by completing the square x^2 +2x+5=0 .
- 1 Educator Answer
- exponential equatione^(3x-4) - 1/e^(x-12)=0
- 1 Educator Answer
- simultaneous equations Solve the simultaneous equations: x^2+y^2=200- xy x+y=20-(xy)^(1/2)
- 1 Educator Answer
- quadratic applicationProve that (2x-1)^2-(x-3)^2 = (3x-4)(x+2).
- 1 Educator Answer
- Solve the equation 1/1024=4*16^2x?
- 1 Educator Answer
One method is to complete the square
x^2 + 3x + _
We'll use the formula for a binomial raised to square:
(a+b)^2 = a^2 + 2ab + b^2
Let a = x => 2xb = 3x => b = 3/2
b^2 = 9/4
To get a perfect square, we'll add and subtract 9/4:
(x^2 + 3x + 9/4) - 9/4 – 4 = 0
(x + 3/2)^2 - 25/4 = 0
We'll get a difference of squares:
a^2 - b^2 = (a-b)(a+b)
We'll put a = x + 3/2
b = 5/2
(x + 3/2)^2 - 25/4 = (x + 3/2 - 5/2)(x + 3/2 + 5/2)
(x + 3/2 - 5/2)(x + 3/2 + 5/2) = 0
We'll put each factor as zero:
x + 3/2 - 5/2 = 0
We'll combine like terms:
x - 2/2 = 0
x - 1 = 0
x = 1
x + 3/2 + 5/2 = 0
x + 8/2 = 0
x + 4 = 0
x = -4
The requested solutions of the equation are {-4 ; 1}.
Student Answers