3x-2 = 25

9        3x-2

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2 Answers

I will give you an example for this question. This might be able to help you.

Simplifying
3x2 + 25x = 18

Reorder the terms:
25x + 3x2 = 18

Solving
25x + 3x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 25x + 3x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 25x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -3x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-9, 0.6666666667}

by Level 10 User (57.4k points)

Problem: Whats 3x-2 over 9 equals 25 over 3x-2?

(3x - 2)/9 = 25/(3x - 2)
(3x - 2) * ((3x - 2)/9) = (25/(3x - 2)) * (3x - 2)
((3x - 2)^2)/9 = 25
9 * ((3x - 2)^2)/9 = 25 * 9
(3x - 2)^2 = 225
(3x - 2)(3x - 2) = 225
9x^2 - 6x - 6x + 4 = 225
9x^2 - 12x + 4 = 225
9x^2 - 12x + 4 - 225 = 225 - 225
9x^2 - 12x - 221 = 0

Use the quadratic equation to solve.

       -b ± sqrt(b² - 4*a*c)
x = ----------------------------
              2a

       -(-12) ± sqrt(-12² - 4*9*(-221))
x = -----------------------------------------
                     2(9)

      12 ± sqrt(144 + 7956)
x = -------------------------------
                18

      12 ± sqrt(8100)
x = ----------------------
              18

       12 ± 90
x = ------------
          18

      12 + 90                     12 - 90
x = ------------    and  x = ------------
          18                            18

      102                     -78
x = -------    and  x = -------
       18                      18

       102                    -78
x = -------    and  x = -------
        18                     18

x = 5.66666    and  x = -4.33333

 

by Level 11 User (78.4k points)

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