4.25x^2-3.17x-6.95=0

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Solution for 4.25x^2-3.17x-6.95=0 equation:


Simplifying
4.25x2 + -3.17x + -6.95 = 0

Reorder the terms:
-6.95 + -3.17x + 4.25x2 = 0

Solving
-6.95 + -3.17x + 4.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.25'.
-1.635294118 + -0.7458823529x + x2 = 0

Move the constant term to the right:

Add '1.635294118' to each side of the equation.
-1.635294118 + -0.7458823529x + 1.635294118 + x2 = 0 + 1.635294118

Reorder the terms:
-1.635294118 + 1.635294118 + -0.7458823529x + x2 = 0 + 1.635294118

Combine like terms: -1.635294118 + 1.635294118 = 0.000000000
0.000000000 + -0.7458823529x + x2 = 0 + 1.635294118
-0.7458823529x + x2 = 0 + 1.635294118

Combine like terms: 0 + 1.635294118 = 1.635294118
-0.7458823529x + x2 = 1.635294118

The x term is -0.7458823529x.  Take half its coefficient (-0.3729411765).
Square it (0.1390851211) and add it to both sides.

Add '0.1390851211' to each side of the equation.
-0.7458823529x + 0.1390851211 + x2 = 1.635294118 + 0.1390851211

Reorder the terms:
0.1390851211 + -0.7458823529x + x2 = 1.635294118 + 0.1390851211

Combine like terms: 1.635294118 + 0.1390851211 = 1.7743792391
0.1390851211 + -0.7458823529x + x2 = 1.7743792391

Factor a perfect square on the left side:
(x + -0.3729411765)(x + -0.3729411765) = 1.7743792391

Calculate the square root of the right side: 1.332058272

Break this problem into two subproblems by setting 
(x + -0.3729411765) equal to 1.332058272 and -1.332058272.

Subproblem 1

x + -0.3729411765 = 1.332058272 Simplifying x + -0.3729411765 = 1.332058272 Reorder the terms: -0.3729411765 + x = 1.332058272 Solving -0.3729411765 + x = 1.332058272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3729411765' to each side of the equation. -0.3729411765 + 0.3729411765 + x = 1.332058272 + 0.3729411765 Combine like terms: -0.3729411765 + 0.3729411765 = 0.0000000000 0.0000000000 + x = 1.332058272 + 0.3729411765 x = 1.332058272 + 0.3729411765 Combine like terms: 1.332058272 + 0.3729411765 = 1.7049994485 x = 1.7049994485 Simplifying x = 1.7049994485

Subproblem 2

x + -0.3729411765 = -1.332058272 Simplifying x + -0.3729411765 = -1.332058272 Reorder the terms: -0.3729411765 + x = -1.332058272 Solving -0.3729411765 + x = -1.332058272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3729411765' to each side of the equation. -0.3729411765 + 0.3729411765 + x = -1.332058272 + 0.3729411765 Combine like terms: -0.3729411765 + 0.3729411765 = 0.0000000000 0.0000000000 + x = -1.332058272 + 0.3729411765 x = -1.332058272 + 0.3729411765 Combine like terms: -1.332058272 + 0.3729411765 = -0.9591170955 x = -0.9591170955 Simplifying x = -0.9591170955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7049994485, -0.9591170955}

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