106x^2+106x=106

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Solution for 106x^2+106x=106 equation:


Simplifying
106x2 + 106x = 106

Reorder the terms:
106x + 106x2 = 106

Solving
106x + 106x2 = 106

Solving for variable 'x'.

Reorder the terms:
-106 + 106x + 106x2 = 106 + -106

Combine like terms: 106 + -106 = 0
-106 + 106x + 106x2 = 0

Factor out the Greatest Common Factor (GCF), '106'.
106(-1 + x + x2) = 0

Ignore the factor 106.

Subproblem 1

Set the factor '(-1 + x + x2)' equal to zero and attempt to solve: Simplifying -1 + x + x2 = 0 Solving -1 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x + x2 = 0 + 1 x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 x + x2 = 1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 1 + 0.25 Reorder the terms: 0.25 + x + x2 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + x + x2 = 1.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 0.5 = 1.118033989 Simplifying x + 0.5 = 1.118033989 Reorder the terms: 0.5 + x = 1.118033989 Solving 0.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.118033989 + -0.5 x = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 x = 0.618033989 Simplifying x = 0.618033989

Subproblem 2

x + 0.5 = -1.118033989 Simplifying x + 0.5 = -1.118033989 Reorder the terms: 0.5 + x = -1.118033989 Solving 0.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.118033989 + -0.5 x = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 x = -1.618033989 Simplifying x = -1.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.618033989, -1.618033989}

Solution

x = {0.618033989, -1.618033989}

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