102=x(2x-3)

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Solution for 102=x(2x-3) equation:


Simplifying
102 = x(2x + -3)

Reorder the terms:
102 = x(-3 + 2x)
102 = (-3 * x + 2x * x)
102 = (-3x + 2x2)

Solving
102 = -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
102 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
102 + 3x + -2x2 = 0 + 2x2 + -2x2
102 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
102 + 3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-51 + -1.5x + x2 = 0

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -1.5x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -1.5x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -1.5x + x2 = 0 + 51
-1.5x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-1.5x + x2 = 51

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 51 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 51 + 0.5625

Combine like terms: 51 + 0.5625 = 51.5625
0.5625 + -1.5x + x2 = 51.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 51.5625

Calculate the square root of the right side: 7.180703308

Break this problem into two subproblems by setting 
(x + -0.75) equal to 7.180703308 and -7.180703308.

Subproblem 1

x + -0.75 = 7.180703308 Simplifying x + -0.75 = 7.180703308 Reorder the terms: -0.75 + x = 7.180703308 Solving -0.75 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.180703308 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.180703308 + 0.75 x = 7.180703308 + 0.75 Combine like terms: 7.180703308 + 0.75 = 7.930703308 x = 7.930703308 Simplifying x = 7.930703308

Subproblem 2

x + -0.75 = -7.180703308 Simplifying x + -0.75 = -7.180703308 Reorder the terms: -0.75 + x = -7.180703308 Solving -0.75 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.180703308 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.180703308 + 0.75 x = -7.180703308 + 0.75 Combine like terms: -7.180703308 + 0.75 = -6.430703308 x = -6.430703308 Simplifying x = -6.430703308

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.930703308, -6.430703308}

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