-2.7x^2+35x+2=0

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Solution for -2.7x^2+35x+2=0 equation:


Simplifying
-2.7x2 + 35x + 2 = 0

Reorder the terms:
2 + 35x + -2.7x2 = 0

Solving
2 + 35x + -2.7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
-0.7407407407 + -12.96296296x + x2 = 0

Move the constant term to the right:

Add '0.7407407407' to each side of the equation.
-0.7407407407 + -12.96296296x + 0.7407407407 + x2 = 0 + 0.7407407407

Reorder the terms:
-0.7407407407 + 0.7407407407 + -12.96296296x + x2 = 0 + 0.7407407407

Combine like terms: -0.7407407407 + 0.7407407407 = 0.0000000000
0.0000000000 + -12.96296296x + x2 = 0 + 0.7407407407
-12.96296296x + x2 = 0 + 0.7407407407

Combine like terms: 0 + 0.7407407407 = 0.7407407407
-12.96296296x + x2 = 0.7407407407

The x term is -12.96296296x.  Take half its coefficient (-6.48148148).
Square it (42.00960218) and add it to both sides.

Add '42.00960218' to each side of the equation.
-12.96296296x + 42.00960218 + x2 = 0.7407407407 + 42.00960218

Reorder the terms:
42.00960218 + -12.96296296x + x2 = 0.7407407407 + 42.00960218

Combine like terms: 0.7407407407 + 42.00960218 = 42.7503429207
42.00960218 + -12.96296296x + x2 = 42.7503429207

Factor a perfect square on the left side:
(x + -6.48148148)(x + -6.48148148) = 42.7503429207

Calculate the square root of the right side: 6.538374639

Break this problem into two subproblems by setting 
(x + -6.48148148) equal to 6.538374639 and -6.538374639.

Subproblem 1

x + -6.48148148 = 6.538374639 Simplifying x + -6.48148148 = 6.538374639 Reorder the terms: -6.48148148 + x = 6.538374639 Solving -6.48148148 + x = 6.538374639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + x = 6.538374639 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + x = 6.538374639 + 6.48148148 x = 6.538374639 + 6.48148148 Combine like terms: 6.538374639 + 6.48148148 = 13.019856119 x = 13.019856119 Simplifying x = 13.019856119

Subproblem 2

x + -6.48148148 = -6.538374639 Simplifying x + -6.48148148 = -6.538374639 Reorder the terms: -6.48148148 + x = -6.538374639 Solving -6.48148148 + x = -6.538374639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + x = -6.538374639 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + x = -6.538374639 + 6.48148148 x = -6.538374639 + 6.48148148 Combine like terms: -6.538374639 + 6.48148148 = -0.056893159 x = -0.056893159 Simplifying x = -0.056893159

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.019856119, -0.056893159}

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