7x^2-16x-20=0

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Solution for 7x^2-16x-20=0 equation:


Simplifying
7x2 + -16x + -20 = 0

Reorder the terms:
-20 + -16x + 7x2 = 0

Solving
-20 + -16x + 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'.
-2.857142857 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + -2.285714286x + 2.857142857 + x2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + -2.285714286x + x2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + -2.285714286x + x2 = 0 + 2.857142857
-2.285714286x + x2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
-2.285714286x + x2 = 2.857142857

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = 2.857142857 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = 2.857142857 + 1.306122449

Combine like terms: 2.857142857 + 1.306122449 = 4.163265306
1.306122449 + -2.285714286x + x2 = 4.163265306

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 4.163265306

Calculate the square root of the right side: 2.040408122

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 2.040408122 and -2.040408122.

Subproblem 1

x + -1.142857143 = 2.040408122 Simplifying x + -1.142857143 = 2.040408122 Reorder the terms: -1.142857143 + x = 2.040408122 Solving -1.142857143 + x = 2.040408122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 2.040408122 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 2.040408122 + 1.142857143 x = 2.040408122 + 1.142857143 Combine like terms: 2.040408122 + 1.142857143 = 3.183265265 x = 3.183265265 Simplifying x = 3.183265265

Subproblem 2

x + -1.142857143 = -2.040408122 Simplifying x + -1.142857143 = -2.040408122 Reorder the terms: -1.142857143 + x = -2.040408122 Solving -1.142857143 + x = -2.040408122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -2.040408122 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -2.040408122 + 1.142857143 x = -2.040408122 + 1.142857143 Combine like terms: -2.040408122 + 1.142857143 = -0.897550979 x = -0.897550979 Simplifying x = -0.897550979

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.183265265, -0.897550979}

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