7x^2+3x-28=0

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Solution for 7x^2+3x-28=0 equation:


Simplifying
7x2 + 3x + -28 = 0

Reorder the terms:
-28 + 3x + 7x2 = 0

Solving
-28 + 3x + 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'.
-4 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.4285714286x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.4285714286x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.4285714286x + x2 = 0 + 4
0.4285714286x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.4285714286x + x2 = 4

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 4 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 4 + 0.04591836735

Combine like terms: 4 + 0.04591836735 = 4.04591836735
0.04591836735 + 0.4285714286x + x2 = 4.04591836735

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 4.04591836735

Calculate the square root of the right side: 2.011446834

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 2.011446834 and -2.011446834.

Subproblem 1

x + 0.2142857143 = 2.011446834 Simplifying x + 0.2142857143 = 2.011446834 Reorder the terms: 0.2142857143 + x = 2.011446834 Solving 0.2142857143 + x = 2.011446834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 2.011446834 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 2.011446834 + -0.2142857143 x = 2.011446834 + -0.2142857143 Combine like terms: 2.011446834 + -0.2142857143 = 1.7971611197 x = 1.7971611197 Simplifying x = 1.7971611197

Subproblem 2

x + 0.2142857143 = -2.011446834 Simplifying x + 0.2142857143 = -2.011446834 Reorder the terms: 0.2142857143 + x = -2.011446834 Solving 0.2142857143 + x = -2.011446834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -2.011446834 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -2.011446834 + -0.2142857143 x = -2.011446834 + -0.2142857143 Combine like terms: -2.011446834 + -0.2142857143 = -2.2257325483 x = -2.2257325483 Simplifying x = -2.2257325483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7971611197, -2.2257325483}

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