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Simplifying 9x2 + 3x + -14 = 0 Reorder the terms: -14 + 3x + 9x2 = 0 Solving -14 + 3x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 0.3333333333x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 0.3333333333x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 1.555555556 0.3333333333x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 0.3333333333x + x2 = 1.555555556 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 1.555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1.555555556 + 0.02777777779 Combine like terms: 1.555555556 + 0.02777777779 = 1.58333333379 0.02777777779 + 0.3333333333x + x2 = 1.58333333379 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.58333333379 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.258305739 and -1.258305739.Subproblem 1
x + 0.1666666667 = 1.258305739 Simplifying x + 0.1666666667 = 1.258305739 Reorder the terms: 0.1666666667 + x = 1.258305739 Solving 0.1666666667 + x = 1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.258305739 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.258305739 + -0.1666666667 x = 1.258305739 + -0.1666666667 Combine like terms: 1.258305739 + -0.1666666667 = 1.0916390723 x = 1.0916390723 Simplifying x = 1.0916390723Subproblem 2
x + 0.1666666667 = -1.258305739 Simplifying x + 0.1666666667 = -1.258305739 Reorder the terms: 0.1666666667 + x = -1.258305739 Solving 0.1666666667 + x = -1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.258305739 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.258305739 + -0.1666666667 x = -1.258305739 + -0.1666666667 Combine like terms: -1.258305739 + -0.1666666667 = -1.4249724057 x = -1.4249724057 Simplifying x = -1.4249724057Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0916390723, -1.4249724057}
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