16x² = 56x - 49?

[03]
16x^2=56x-49
16x^2-56x= -49
(4x)^2-2*4x*7+(7)^2=-49+49 [adding 7^2 or 49 to both sides]
(4x-7)^2=0
4x-7=0
4x=7
x=7/4

16 x ² - 56 x + 49 = 0
(4x - 7) (4x - 7) = 0
x = 7 / 4

16x² - 56x + 49 = 0
=> (4x-7)^2 = 0
=> x = 7/4
------------
Ideas: (a-b)^2 = a^2-2ab+b^2,
So, 16x^2 = (4x)^2, 49 = 7^2, and -2(4x)(7) = -56x.

16x^2 = 56x - 49
0 = 56x - 49 - 16x^2
0 = -16x^2 + 56x - 49
-16x^2 + 56x - 49 = 0
(-4x + 7)(4x - 7) = 0
(4x - 7)^2 = 0
x = 1.75

16x² = 56x - 49?
16x² - 56x + 49=0
16x² - 28x-28x + 49=0
4x(4x-7)-7(4x-7)=0
4x-7=0
4x=7
x=7/4

16x² = 56x – 49
16x² – 56x + 49 = 0
square root of 1st term 16x^2 = 4x
square root of 3rd term 49 = 7
Middle term = 2 × 4x × 7 = 56 x
so the given expression is a perfect square.
16x² – 56x + 49 = 0
(4 x – 7)^2 = 0
(4 x – 7) = 0
4 x = 7
x = 7/4

Given: 16x² = 56x - 49
Required: find x or factor?

Solution:

Step 1: transform the equation into Quadratic Form, ax + bx + c = 0

thus,

16x² - 56x + 49 = 0 -------->>>> Quadratic form (1)

Step2: Look for the coefficients of x^2, x and constant c.

a = 16
b = - 56
c = 49

Step3. Use the Quadratic formula x(±) = [- b ± (b^2 - 4ac)^(1/2)]/2a to find for the values of x. There are 2 values of x, x(+) and x(-) (symbolized as x(±))

Step4: Substitute known coefficients of x^2, x and constant c to the Quadratic formula at step3.

x(±) = {- (-56) ± [(-56)^2 - 4(16)(49)]^(1/2)}/2(16)
x(±) = [56 ± (3,136 - 3,136)^(1/2)]/32
x(±) = 56/32 = 7/4

x(+) = 7/4
x(-) = 7/4

If you are looking for the value of x
x = 7/4 ------>>>> Answer


Or if you are looking for the factor of the equation (1) above, go to the following step...

Step5: You can now get the factor of the equation by

(x - 7/4)(x - 7/4) = 0

or

(4x - 7) (4x - 7) = 0 ------>>>> answer

It's easy: 16(squareX)-56X+49=0

Ans apply the formule: (-b +/- b(square)-4.a.c)/2.a

=> 16x^2 - 56x + 49 = 0
consider (a - b)^2 = a^2 - 2ab + b^2
=> (4x)^2 - 2 * 4 * 7 *x + 7^2 = 0
=> a = 4x, b = 7
=> (4x - 7)^2 = 0