=-4.9x^2+14x+2.1

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Solution for =-4.9x^2+14x+2.1 equation:


Simplifying
0 = -4.9x2 + 14x + 2.1

Reorder the terms:
0 = 2.1 + 14x + -4.9x2

Solving
0 = 2.1 + 14x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -2.1 = -2.1
-2.1 + -14x + 4.9x2 = 2.1 + 14x + -4.9x2 + -2.1 + -14x + 4.9x2

Reorder the terms:
-2.1 + -14x + 4.9x2 = 2.1 + -2.1 + 14x + -14x + -4.9x2 + 4.9x2

Combine like terms: 2.1 + -2.1 = 0.0
-2.1 + -14x + 4.9x2 = 0.0 + 14x + -14x + -4.9x2 + 4.9x2
-2.1 + -14x + 4.9x2 = 14x + -14x + -4.9x2 + 4.9x2

Combine like terms: 14x + -14x = 0
-2.1 + -14x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-2.1 + -14x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-2.1 + -14x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
-0.4285714286 + -2.857142857x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -2.857142857x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -2.857142857x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -2.857142857x + x2 = 0 + 0.4285714286
-2.857142857x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-2.857142857x + x2 = 0.4285714286

The x term is -2.857142857x.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857x + 2.040816328 + x2 = 0.4285714286 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857x + x2 = 0.4285714286 + 2.040816328

Combine like terms: 0.4285714286 + 2.040816328 = 2.4693877566
2.040816328 + -2.857142857x + x2 = 2.4693877566

Factor a perfect square on the left side:
(x + -1.428571429)(x + -1.428571429) = 2.4693877566

Calculate the square root of the right side: 1.571428572

Break this problem into two subproblems by setting 
(x + -1.428571429) equal to 1.571428572 and -1.571428572.

Subproblem 1

x + -1.428571429 = 1.571428572 Simplifying x + -1.428571429 = 1.571428572 Reorder the terms: -1.428571429 + x = 1.571428572 Solving -1.428571429 + x = 1.571428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.571428572 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.571428572 + 1.428571429 x = 1.571428572 + 1.428571429 Combine like terms: 1.571428572 + 1.428571429 = 3.000000001 x = 3.000000001 Simplifying x = 3.000000001

Subproblem 2

x + -1.428571429 = -1.571428572 Simplifying x + -1.428571429 = -1.571428572 Reorder the terms: -1.428571429 + x = -1.571428572 Solving -1.428571429 + x = -1.571428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.571428572 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.571428572 + 1.428571429 x = -1.571428572 + 1.428571429 Combine like terms: -1.571428572 + 1.428571429 = -0.142857143 x = -0.142857143 Simplifying x = -0.142857143

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.000000001, -0.142857143}

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