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Simplifying 9x2 + 6x + -107 = 0 Reorder the terms: -107 + 6x + 9x2 = 0 Solving -107 + 6x + 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'. -11.88888889 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '11.88888889' to each side of the equation. -11.88888889 + 0.6666666667x + 11.88888889 + x2 = 0 + 11.88888889 Reorder the terms: -11.88888889 + 11.88888889 + 0.6666666667x + x2 = 0 + 11.88888889 Combine like terms: -11.88888889 + 11.88888889 = 0.00000000 0.00000000 + 0.6666666667x + x2 = 0 + 11.88888889 0.6666666667x + x2 = 0 + 11.88888889 Combine like terms: 0 + 11.88888889 = 11.88888889 0.6666666667x + x2 = 11.88888889 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 11.88888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 11.88888889 + 0.1111111112 Combine like terms: 11.88888889 + 0.1111111112 = 12.0000000012 0.1111111112 + 0.6666666667x + x2 = 12.0000000012 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 12.0000000012 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 0.3333333334 = 3.464101615 Simplifying x + 0.3333333334 = 3.464101615 Reorder the terms: 0.3333333334 + x = 3.464101615 Solving 0.3333333334 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 3.464101615 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.464101615 + -0.3333333334 x = 3.464101615 + -0.3333333334 Combine like terms: 3.464101615 + -0.3333333334 = 3.1307682816 x = 3.1307682816 Simplifying x = 3.1307682816Subproblem 2
x + 0.3333333334 = -3.464101615 Simplifying x + 0.3333333334 = -3.464101615 Reorder the terms: 0.3333333334 + x = -3.464101615 Solving 0.3333333334 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -3.464101615 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.464101615 + -0.3333333334 x = -3.464101615 + -0.3333333334 Combine like terms: -3.464101615 + -0.3333333334 = -3.7974349484 x = -3.7974349484 Simplifying x = -3.7974349484Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1307682816, -3.7974349484}
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