966x+966x^2=56

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Solution for 966x+966x^2=56 equation:


Simplifying
966x + 966x2 = 56

Solving
966x + 966x2 = 56

Solving for variable 'x'.

Reorder the terms:
-56 + 966x + 966x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 966x + 966x2 = 0

Factor out the Greatest Common Factor (GCF), '14'.
14(-4 + 69x + 69x2) = 0

Ignore the factor 14.

Subproblem 1

Set the factor '(-4 + 69x + 69x2)' equal to zero and attempt to solve: Simplifying -4 + 69x + 69x2 = 0 Solving -4 + 69x + 69x2 = 0 Begin completing the square. Divide all terms by 69 the coefficient of the squared term: Divide each side by '69'. -0.05797101449 + x + x2 = 0 Move the constant term to the right: Add '0.05797101449' to each side of the equation. -0.05797101449 + x + 0.05797101449 + x2 = 0 + 0.05797101449 Reorder the terms: -0.05797101449 + 0.05797101449 + x + x2 = 0 + 0.05797101449 Combine like terms: -0.05797101449 + 0.05797101449 = 0.00000000000 0.00000000000 + x + x2 = 0 + 0.05797101449 x + x2 = 0 + 0.05797101449 Combine like terms: 0 + 0.05797101449 = 0.05797101449 x + x2 = 0.05797101449 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. + 0.25 + x2 = 0.05797101449 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.05797101449 + 0.25 Combine like terms: 0.05797101449 + 0.25 = 0.30797101449 1.25 + x2 = 0.30797101449 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.30797101449 Calculate the square root of the right side: 0.554951362 Break this problem into two subproblems by setting (x + 0.5) equal to 0.554951362 and -0.554951362.

Subproblem 1

x + 0.5 = 0.554951362 Simplifying x + 0.5 = 0.554951362 Reorder the terms: 0.5 + x = 0.554951362 Solving 0.5 + x = 0.554951362 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 = 0.554951362 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.554951362 + -0.5 x = 0.554951362 + -0.5 Combine like terms: 0.554951362 + -0.5 = 0.054951362 x = 0.054951362 Simplifying x = 0.054951362

Subproblem 2

x + 0.5 = -0.554951362 Simplifying x + 0.5 = -0.554951362 Reorder the terms: 0.5 + x = -0.554951362 Solving 0.5 + x = -0.554951362 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 = -0.554951362 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.554951362 + -0.5 x = -0.554951362 + -0.5 Combine like terms: -0.554951362 + -0.5 = -1.054951362 x = -1.054951362 Simplifying x = -1.054951362

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.054951362, -1.054951362}

Solution

x = {0.054951362, -1.054951362}

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