-7x^2+12x-2=0

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Solution for -7x^2+12x-2=0 equation:


Simplifying
-7x2 + 12x + -2 = 0

Reorder the terms:
-2 + 12x + -7x2 = 0

Solving
-2 + 12x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.2857142857 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -1.714285714x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -1.714285714x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.2857142857
-1.714285714x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-1.714285714x + x2 = -0.2857142857

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.2857142857 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.2857142857 + 0.7346938773

Combine like terms: -0.2857142857 + 0.7346938773 = 0.4489795916
0.7346938773 + -1.714285714x + x2 = 0.4489795916

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.4489795916

Calculate the square root of the right side: 0.670059394

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.670059394 and -0.670059394.

Subproblem 1

x + -0.857142857 = 0.670059394 Simplifying x + -0.857142857 = 0.670059394 Reorder the terms: -0.857142857 + x = 0.670059394 Solving -0.857142857 + x = 0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 0.670059394 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.670059394 + 0.857142857 x = 0.670059394 + 0.857142857 Combine like terms: 0.670059394 + 0.857142857 = 1.527202251 x = 1.527202251 Simplifying x = 1.527202251

Subproblem 2

x + -0.857142857 = -0.670059394 Simplifying x + -0.857142857 = -0.670059394 Reorder the terms: -0.857142857 + x = -0.670059394 Solving -0.857142857 + x = -0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -0.670059394 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.670059394 + 0.857142857 x = -0.670059394 + 0.857142857 Combine like terms: -0.670059394 + 0.857142857 = 0.187083463 x = 0.187083463 Simplifying x = 0.187083463

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.527202251, 0.187083463}

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