Solve the equation 4x2 + 12x - 7= 0 by completing the square method
Answers
hi mate,
solution: Factoring 4x²+12x-7
4x²- 2x + 14x - 7
Step-1 : Add up the first 2 terms, pulling out like factors :
2x • (2x-1)
Add up the last 2 terms, pulling out common factors :
7 • (2x-1)
Step-2: Add up the four terms of step 1 :
(2x+7) • (2x-1)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 1) • (2x + 7) = 0
OR
Solving 4x2+12x-7 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B²-4AC
x = ————————
2A
In our case, A = 4
B = 12
C = -7
Accordingly, B² - 4AC =
144 - (-112) =
256
Applying the quadratic formula :
-12 ± √ 256
x = ——————
8
Can √ 256 be simplified ?
Yes! The prime factorization of 256 is
2•2•2•2•2•2•2•2
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 256 = √ 2•2•2•2•2•2•2•2 =2•2•2•2•√ 1 =
± 16 • √ 1 =
± 16
So now we are looking at:
x = ( -12 ± 16) / 8
Two real solutions:
x =(-12+√256)/8=-3/2+2= 0.500
or:
x =(-12-√256)/8=-3/2-2= -3.500
Two solutions were found :
x = -7/2 = -3.500
x = 1/2 = 0.500
i hope it helps you.