7x^2-11=28x+86

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Solution for 7x^2-11=28x+86 equation:


Simplifying
7x2 + -11 = 28x + 86

Reorder the terms:
-11 + 7x2 = 28x + 86

Reorder the terms:
-11 + 7x2 = 86 + 28x

Solving
-11 + 7x2 = 86 + 28x

Solving for variable 'x'.

Reorder the terms:
-11 + -86 + -28x + 7x2 = 86 + 28x + -86 + -28x

Combine like terms: -11 + -86 = -97
-97 + -28x + 7x2 = 86 + 28x + -86 + -28x

Reorder the terms:
-97 + -28x + 7x2 = 86 + -86 + 28x + -28x

Combine like terms: 86 + -86 = 0
-97 + -28x + 7x2 = 0 + 28x + -28x
-97 + -28x + 7x2 = 28x + -28x

Combine like terms: 28x + -28x = 0
-97 + -28x + 7x2 = 0

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

Divide each side by '7'.
-13.85714286 + -4x + x2 = 0

Move the constant term to the right:

Add '13.85714286' to each side of the equation.
-13.85714286 + -4x + 13.85714286 + x2 = 0 + 13.85714286

Reorder the terms:
-13.85714286 + 13.85714286 + -4x + x2 = 0 + 13.85714286

Combine like terms: -13.85714286 + 13.85714286 = 0.00000000
0.00000000 + -4x + x2 = 0 + 13.85714286
-4x + x2 = 0 + 13.85714286

Combine like terms: 0 + 13.85714286 = 13.85714286
-4x + x2 = 13.85714286

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 13.85714286 + 4

Reorder the terms:
4 + -4x + x2 = 13.85714286 + 4

Combine like terms: 13.85714286 + 4 = 17.85714286
4 + -4x + x2 = 17.85714286

Factor a perfect square on the left side:
(x + -2)(x + -2) = 17.85714286

Calculate the square root of the right side: 4.225771274

Break this problem into two subproblems by setting 
(x + -2) equal to 4.225771274 and -4.225771274.

Subproblem 1

x + -2 = 4.225771274 Simplifying x + -2 = 4.225771274 Reorder the terms: -2 + x = 4.225771274 Solving -2 + x = 4.225771274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.225771274 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.225771274 + 2 x = 4.225771274 + 2 Combine like terms: 4.225771274 + 2 = 6.225771274 x = 6.225771274 Simplifying x = 6.225771274

Subproblem 2

x + -2 = -4.225771274 Simplifying x + -2 = -4.225771274 Reorder the terms: -2 + x = -4.225771274 Solving -2 + x = -4.225771274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.225771274 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.225771274 + 2 x = -4.225771274 + 2 Combine like terms: -4.225771274 + 2 = -2.225771274 x = -2.225771274 Simplifying x = -2.225771274

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.225771274, -2.225771274}

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