-4.1x^2+7.1x+145=0

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Solution for -4.1x^2+7.1x+145=0 equation:


Simplifying
-4.1x2 + 7.1x + 145 = 0

Reorder the terms:
145 + 7.1x + -4.1x2 = 0

Solving
145 + 7.1x + -4.1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.1 the coefficient of the squared term: 

Divide each side by '-4.1'.
-35.36585366 + -1.731707317x + x2 = 0

Move the constant term to the right:

Add '35.36585366' to each side of the equation.
-35.36585366 + -1.731707317x + 35.36585366 + x2 = 0 + 35.36585366

Reorder the terms:
-35.36585366 + 35.36585366 + -1.731707317x + x2 = 0 + 35.36585366

Combine like terms: -35.36585366 + 35.36585366 = 0.00000000
0.00000000 + -1.731707317x + x2 = 0 + 35.36585366
-1.731707317x + x2 = 0 + 35.36585366

Combine like terms: 0 + 35.36585366 = 35.36585366
-1.731707317x + x2 = 35.36585366

The x term is -1.731707317x.  Take half its coefficient (-0.8658536585).
Square it (0.7497025579) and add it to both sides.

Add '0.7497025579' to each side of the equation.
-1.731707317x + 0.7497025579 + x2 = 35.36585366 + 0.7497025579

Reorder the terms:
0.7497025579 + -1.731707317x + x2 = 35.36585366 + 0.7497025579

Combine like terms: 35.36585366 + 0.7497025579 = 36.1155562179
0.7497025579 + -1.731707317x + x2 = 36.1155562179

Factor a perfect square on the left side:
(x + -0.8658536585)(x + -0.8658536585) = 36.1155562179

Calculate the square root of the right side: 6.00962197

Break this problem into two subproblems by setting 
(x + -0.8658536585) equal to 6.00962197 and -6.00962197.

Subproblem 1

x + -0.8658536585 = 6.00962197 Simplifying x + -0.8658536585 = 6.00962197 Reorder the terms: -0.8658536585 + x = 6.00962197 Solving -0.8658536585 + x = 6.00962197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8658536585' to each side of the equation. -0.8658536585 + 0.8658536585 + x = 6.00962197 + 0.8658536585 Combine like terms: -0.8658536585 + 0.8658536585 = 0.0000000000 0.0000000000 + x = 6.00962197 + 0.8658536585 x = 6.00962197 + 0.8658536585 Combine like terms: 6.00962197 + 0.8658536585 = 6.8754756285 x = 6.8754756285 Simplifying x = 6.8754756285

Subproblem 2

x + -0.8658536585 = -6.00962197 Simplifying x + -0.8658536585 = -6.00962197 Reorder the terms: -0.8658536585 + x = -6.00962197 Solving -0.8658536585 + x = -6.00962197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8658536585' to each side of the equation. -0.8658536585 + 0.8658536585 + x = -6.00962197 + 0.8658536585 Combine like terms: -0.8658536585 + 0.8658536585 = 0.0000000000 0.0000000000 + x = -6.00962197 + 0.8658536585 x = -6.00962197 + 0.8658536585 Combine like terms: -6.00962197 + 0.8658536585 = -5.1437683115 x = -5.1437683115 Simplifying x = -5.1437683115

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.8754756285, -5.1437683115}

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