3(2x*2x-3)=25x

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Solution for 3(2x*2x-3)=25x equation:


Simplifying
3(2x * 2x + -3) = 25x

Reorder the terms for easier multiplication:
3(2 * 2x * x + -3) = 25x

Multiply 2 * 2
3(4x * x + -3) = 25x

Multiply x * x
3(4x2 + -3) = 25x

Reorder the terms:
3(-3 + 4x2) = 25x
(-3 * 3 + 4x2 * 3) = 25x
(-9 + 12x2) = 25x

Solving
-9 + 12x2 = 25x

Solving for variable 'x'.

Reorder the terms:
-9 + -25x + 12x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
-9 + -25x + 12x2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
-0.75 + -2.083333333x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -2.083333333x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -2.083333333x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -2.083333333x + x2 = 0 + 0.75
-2.083333333x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-2.083333333x + x2 = 0.75

The x term is -2.083333333x.  Take half its coefficient (-1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
-2.083333333x + 1.085069445 + x2 = 0.75 + 1.085069445

Reorder the terms:
1.085069445 + -2.083333333x + x2 = 0.75 + 1.085069445

Combine like terms: 0.75 + 1.085069445 = 1.835069445
1.085069445 + -2.083333333x + x2 = 1.835069445

Factor a perfect square on the left side:
(x + -1.041666667)(x + -1.041666667) = 1.835069445

Calculate the square root of the right side: 1.354647351

Break this problem into two subproblems by setting 
(x + -1.041666667) equal to 1.354647351 and -1.354647351.

Subproblem 1

x + -1.041666667 = 1.354647351 Simplifying x + -1.041666667 = 1.354647351 Reorder the terms: -1.041666667 + x = 1.354647351 Solving -1.041666667 + x = 1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 1.354647351 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 1.354647351 + 1.041666667 x = 1.354647351 + 1.041666667 Combine like terms: 1.354647351 + 1.041666667 = 2.396314018 x = 2.396314018 Simplifying x = 2.396314018

Subproblem 2

x + -1.041666667 = -1.354647351 Simplifying x + -1.041666667 = -1.354647351 Reorder the terms: -1.041666667 + x = -1.354647351 Solving -1.041666667 + x = -1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -1.354647351 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -1.354647351 + 1.041666667 x = -1.354647351 + 1.041666667 Combine like terms: -1.354647351 + 1.041666667 = -0.312980684 x = -0.312980684 Simplifying x = -0.312980684

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.396314018, -0.312980684}

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