2x^2-15x+6=41

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Solution for 2x^2-15x+6=41 equation:


Simplifying
2x2 + -15x + 6 = 41

Reorder the terms:
6 + -15x + 2x2 = 41

Solving
6 + -15x + 2x2 = 41

Solving for variable 'x'.

Reorder the terms:
6 + -41 + -15x + 2x2 = 41 + -41

Combine like terms: 6 + -41 = -35
-35 + -15x + 2x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-35 + -15x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -7.5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -7.5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -7.5x + x2 = 0 + 17.5
-7.5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-7.5x + x2 = 17.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 17.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 17.5 + 14.0625

Combine like terms: 17.5 + 14.0625 = 31.5625
14.0625 + -7.5x + x2 = 31.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(x + -3.75) equal to 5.618051264 and -5.618051264.

Subproblem 1

x + -3.75 = 5.618051264 Simplifying x + -3.75 = 5.618051264 Reorder the terms: -3.75 + x = 5.618051264 Solving -3.75 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.618051264 + 3.75 x = 5.618051264 + 3.75 Combine like terms: 5.618051264 + 3.75 = 9.368051264 x = 9.368051264 Simplifying x = 9.368051264

Subproblem 2

x + -3.75 = -5.618051264 Simplifying x + -3.75 = -5.618051264 Reorder the terms: -3.75 + x = -5.618051264 Solving -3.75 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.618051264 + 3.75 x = -5.618051264 + 3.75 Combine like terms: -5.618051264 + 3.75 = -1.868051264 x = -1.868051264 Simplifying x = -1.868051264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.368051264, -1.868051264}

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