2x² - 1 = 17 in quadratic equation

TWO SOLUTIONS:

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*x^2-1-(17)=0

Step by step solution : STEP 1:

Equation at the end of step 1

 (2x2 -  1) -  17  = 0

STEP 2 :

Pulling out like terms

3.1     Pull out like factors :

  2x2 - 18  =   2 • (x2 - 9)

Trying to factor as a Difference of Squares:

3.2      Factoring:  x2 - 9

Theory : A difference of two perfect squares,  A2 - B2  can be factored into (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check :  x2  is the square of  x1

Factorization is :      (x + 3)  •  (x - 3)

Equation at the end of step 2:

 2 • (x + 3) • (x - 3)  = 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.

Equations which are never true:

3.2      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    x+3 = 0

Subtract  3  from both sides of the equation :

                     x = -3

Solving a Single Variable Equation:

4.4      Solve  :    x-3 = 0

Add  3  to both sides of the equation :

                     x = 3

$12. that is my answer.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.