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Simplifying 9x * x + 14x = 14 Multiply x * x 9x2 + 14x = 14 Reorder the terms: 14x + 9x2 = 14 Solving 14x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 14x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 14x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 1.555555556x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 1.555555556x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 1.555555556x + x2 = 0 + 1.555555556 1.555555556x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 1.555555556x + x2 = 1.555555556 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 1.555555556 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 1.555555556 + 0.6049382720 Combine like terms: 1.555555556 + 0.6049382720 = 2.160493828 0.6049382720 + 1.555555556x + x2 = 2.160493828 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 2.160493828 Calculate the square root of the right side: 1.46986184 Break this problem into two subproblems by setting (x + 0.777777778) equal to 1.46986184 and -1.46986184.Subproblem 1
x + 0.777777778 = 1.46986184 Simplifying x + 0.777777778 = 1.46986184 Reorder the terms: 0.777777778 + x = 1.46986184 Solving 0.777777778 + x = 1.46986184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.46986184 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.46986184 + -0.777777778 x = 1.46986184 + -0.777777778 Combine like terms: 1.46986184 + -0.777777778 = 0.692084062 x = 0.692084062 Simplifying x = 0.692084062Subproblem 2
x + 0.777777778 = -1.46986184 Simplifying x + 0.777777778 = -1.46986184 Reorder the terms: 0.777777778 + x = -1.46986184 Solving 0.777777778 + x = -1.46986184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.46986184 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.46986184 + -0.777777778 x = -1.46986184 + -0.777777778 Combine like terms: -1.46986184 + -0.777777778 = -2.247639618 x = -2.247639618 Simplifying x = -2.247639618Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.692084062, -2.247639618}
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