3x^2-15x=10

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Solution for 3x^2-15x=10 equation:


Simplifying
3x2 + -15x = 10

Reorder the terms:
-15x + 3x2 = 10

Solving
-15x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -15x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -15x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + 3.333333333
-5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-5x + x2 = 3.333333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 3.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3.333333333 + 6.25

Combine like terms: 3.333333333 + 6.25 = 9.583333333
6.25 + -5x + x2 = 9.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.583333333

Calculate the square root of the right side: 3.095695937

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.095695937 and -3.095695937.

Subproblem 1

x + -2.5 = 3.095695937 Simplifying x + -2.5 = 3.095695937 Reorder the terms: -2.5 + x = 3.095695937 Solving -2.5 + x = 3.095695937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.095695937 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.095695937 + 2.5 x = 3.095695937 + 2.5 Combine like terms: 3.095695937 + 2.5 = 5.595695937 x = 5.595695937 Simplifying x = 5.595695937

Subproblem 2

x + -2.5 = -3.095695937 Simplifying x + -2.5 = -3.095695937 Reorder the terms: -2.5 + x = -3.095695937 Solving -2.5 + x = -3.095695937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.095695937 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.095695937 + 2.5 x = -3.095695937 + 2.5 Combine like terms: -3.095695937 + 2.5 = -0.595695937 x = -0.595695937 Simplifying x = -0.595695937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.595695937, -0.595695937}

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