Question

48x^2-13x-1=0 by using squaring method

Answer 1

48x²-13x-1=0 Two solutions were found :

1. x = -1/16 = -0.063
2. x = 1/3 = 0.333

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution : Step 1 : Equation at the end of step 1 : ((2⁴•3x²) - 13x) - 1 = 0 Step 2 : Trying to factor by splitting the middle term

2.1 Factoring 48x²-13x-1

The first term is, 48x² its coefficient is 48 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 48 • -1 = -48

Step-2 : Find two factors of -48 whose sum equals the coefficient of the middle term, which is -13 .

	-48	+	1	=	-47
	-24	+	2	=	-22
	-16	+	3	=	-13	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 3
48x² - 16x + 3x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
16x • (3x-1)
Add up the last 2 terms, pulling out common factors :
1 • (3x-1)
Step-5 : Add up the four terms of step 4 :
(16x+1) • (3x-1)
Which is the desired factorization

Equation at the end of step 2 : (3x - 1) • (16x + 1) = 0 Step 3 : Theory - Roots of a product :

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2 Solve : 3x-1 = 0

Add 1 to both sides of the equation :
3x = 1
Divide both sides of the equation by 3:
x = 1/3 = 0.333

Solving a Single Variable Equation :

3.3 Solve : 16x+1 = 0

Subtract 1 from both sides of the equation :
16x = -1
Divide both sides of the equation by 16:
x = -1/16 = -0.063