0.75x^2-25*x+86=0

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Solution for 0.75x^2-25*x+86=0 equation:


Simplifying
0.75x2 + -25x + 86 = 0

Reorder the terms:
86 + -25x + 0.75x2 = 0

Solving
86 + -25x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
114.6666667 + -33.33333333x + x2 = 0

Move the constant term to the right:

Add '-114.6666667' to each side of the equation.
114.6666667 + -33.33333333x + -114.6666667 + x2 = 0 + -114.6666667

Reorder the terms:
114.6666667 + -114.6666667 + -33.33333333x + x2 = 0 + -114.6666667

Combine like terms: 114.6666667 + -114.6666667 = 0.0000000
0.0000000 + -33.33333333x + x2 = 0 + -114.6666667
-33.33333333x + x2 = 0 + -114.6666667

Combine like terms: 0 + -114.6666667 = -114.6666667
-33.33333333x + x2 = -114.6666667

The x term is -33.33333333x.  Take half its coefficient (-16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
-33.33333333x + 277.7777779 + x2 = -114.6666667 + 277.7777779

Reorder the terms:
277.7777779 + -33.33333333x + x2 = -114.6666667 + 277.7777779

Combine like terms: -114.6666667 + 277.7777779 = 163.1111112
277.7777779 + -33.33333333x + x2 = 163.1111112

Factor a perfect square on the left side:
(x + -16.66666667)(x + -16.66666667) = 163.1111112

Calculate the square root of the right side: 12.771496044

Break this problem into two subproblems by setting 
(x + -16.66666667) equal to 12.771496044 and -12.771496044.

Subproblem 1

x + -16.66666667 = 12.771496044 Simplifying x + -16.66666667 = 12.771496044 Reorder the terms: -16.66666667 + x = 12.771496044 Solving -16.66666667 + x = 12.771496044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = 12.771496044 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = 12.771496044 + 16.66666667 x = 12.771496044 + 16.66666667 Combine like terms: 12.771496044 + 16.66666667 = 29.438162714 x = 29.438162714 Simplifying x = 29.438162714

Subproblem 2

x + -16.66666667 = -12.771496044 Simplifying x + -16.66666667 = -12.771496044 Reorder the terms: -16.66666667 + x = -12.771496044 Solving -16.66666667 + x = -12.771496044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = -12.771496044 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = -12.771496044 + 16.66666667 x = -12.771496044 + 16.66666667 Combine like terms: -12.771496044 + 16.66666667 = 3.895170626 x = 3.895170626 Simplifying x = 3.895170626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.438162714, 3.895170626}

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